Abstract: An agent 10 is associated with a user as a representative of the user. The agent 10 includes a utility value calculation unit 15 that calculates an expected utility value indicating utility for the user with respect to an operating condition of the load device 20 and a cooperation processing unit 16 that judges whether an operating condition of the load device 20 is acceptable or not to the user and uniquely determines an operating condition to be instructed to the load device if the operating condition is not acceptable to the user cooperating with other agents 10. Agents 10 that do not accept the operating condition of the load device 20 determine the operating condition of the load device 20 such that one agent acting as a manager and the other agent acting as a contractor so as to make (some) concession to each other.

Abstract: An apparatus, a method, and a non-transitory computer readable storage medium thereof for recommending an electricity consumption behavior are provided. The apparatus is stored with an appliance efficiency value and an electricity-consuming parameter value for each of a plurality of users. The apparatus generates a plurality of first temporary values by multiplying each of the appliance efficiency values with each of the electricity-consuming parameters, generates a power saving matrix by subtracting each of the electricity-consuming parameters from each of the electricity-consuming parameters individually, generates a changing willingness matrix by the second temporary values, calculates a transform probability matrix by the power saving matrix and the changing willingness matrix, calculates an eigenvalue and an eigenvector of the transform probability matrix, and recommends an electricity consumption behavior according to the eigenvalue and the eigenvector.

Abstract: A method for destination and duration of stay determination in a geographically bounded area such as a smart home includes detecting movement by an identified individual in an origination location of a geographically bounded area and retrieving a contemporaneously generated pattern of movement for the individual. The method additionally includes comparing the pattern for the identified individual to a set of patterns in a pattern data store and predicting from a matching pattern both a destination location in the geographically bounded area and a duration of time at which the identified individual is to remain at the destination location. Finally, the method includes directing activation of a fixture at the destination location responsive to predicting the destination location, and directing deactivation of a fixture at the origination location responsive to predicting a duration of time that exceeds a threshold value.

Abstract: In one embodiment, agent routines are executed in a first thread, each agent routine being invoked by one of coroutines. A agent processor executes in a second thread the agents associated with the one or more agent routines, including receiving a first yield signal from a first of the coroutines indicating that a first of the agent routines yields to perform a first action that requires an action simulation, in response to the first yield signal, suspending the first coroutine, selecting a second of the coroutines from a head of a first agent queue maintained by the agent processor, and executing the second coroutine by assigning the execution lock to the second coroutine. In a third thread, a simulator simulates the first action on behalf of the first coroutine and signals the agent processor to resume the first coroutine after completing the simulation of the first action.

Abstract: Integrated methods and systems for optimizing drilling related operations include recording data, parsing the data into intervals and analyzing the intervals to determine if the performance data in each time interval is of sufficient quality for using the interval data in a performance optimization process. The quality assessment may involve evaluating the data against a set of determined standards or ranges. The performance optimization process may utilize data mapping and/or modeling to make performance optimization process recommendations.

Abstract: In an apparatus and a method of evaluating a clamp force (F) in a threaded joint between a bolt and a matching threaded piece during a tightening operation, a torque (T) provided to the joint is continuously measured and ultra-sonic pulses are simultaneously induced into the bolt such that a time of flight (TOF) of the pulses in the bolt is measured. In response to an increase of the measured torque (T) an increase rate (dT/d?) of the torque (T) is determined, from which an initial rotation angle (?0) where the torque (T) starts to increase due to bolt deformation is determined. An increase rate (dTOF/d?) of the time of flight (TOF) is also determined. A total increase of the time of flight (?TOF) during the tightening operation is then determined based on the initial rotation angle (?0) and the increase rate (dTOF/d?) of the time of flight (TOF).

Abstract: The present invention provides an apparatus for stabilizing an imaging device and methods of using the same for a wide variety of applications including photography, video, and filming. Also provided are unmanned vehicles including aerial vehicles that contain the apparatus disclosed herein.

Abstract: In a refrigeration appliance, an enclosure or container defines an enclosed space. A two-plane door forms a portion of the container. The two-plane door opens along one pivot axis and allows access to the enclosed interior space. The container can be a thermally insulated in-door ice compartment of a refrigerated appliance. One example is a bottom freezer style, with the in-door ice compartment in the cold food section of the appliance.

Abstract: A method of controlling a brushless permanent-magnet motor. The method includes commutating a winding of the motor at times relative to zero-crossings of back EMF in the winding. Commutation is then advanced when the motor operates over a first speed range, and commutation is retarded when the motor operates over a second speed range higher than that of the first speed range.

Abstract: A motor driving amplifier and a numerical controller are connected to each other via communication to configure a numerical control system. The numerical controller includes a numerical control unit, a motor control unit, and an amplifier interface unit. Furthermore, a motor control processor included in the motor control unit is a multi-core processor.

Abstract: A method for remote collaboration includes receiving posting content from a first employee of a company. The posting content includes a multitude of key terms. The method further includes generating a first employee posting using the posting content, extracting the multitude of key terms from the posting content, matching one of the plurality of key terms to a key term label, storing the key term label in the first employee posting, and selecting a company channel corresponding to the key terms label. The method further includes identifying a subscriber of the company channel, where the subscriber is a second employee of the company, and presenting the first employee posting content to the subscriber.

Abstract: A method of a hand held torque delivering power tool for tightening a screw joint up to a predetermined target torque level, the method including applying a tightening torque to the screw joint during a tightening phase via a snug torque level, indicating during the tightening phase a torque growth characteristic, interrupting the torque application on the screw joint upon arrival at a target torque level to prevent further rotation of the screw joint, and resuming the torque application via a declination ramp at a declining rate after the target torque level is reached. The resumed torque application is declined at a rate corresponding to the indicated torque growth characteristic to obtain an ergonomically favorable torque reaction characteristic in the power tool.

Abstract: A receptacle is provided to connect modular electronic instruments to each other. A box-shaped case has a front face having an opening for inserting a single modular electronic instrument into the box-shaped case. A first connector is disposed inside the box-shaped case to connect the single modular electronic instrument to the receptacle. A second connector is disposed on a first side face of the receptacle for connecting the receptacle to a first receptacle on the side of the first side face. A third connector is disposed on a second side face of the receptacle for connecting the receptacle to a second receptacle on the side of the second side face. A lock secures the connection with one of the first and second receptacles. A leg is disposed on the bottom face. The position of the leg is deviated only to one of the first or second side faces.

Abstract: A sensor event assessor input/output controller is disclosed. In one embodiment, a multi-channel sensor input configuration provides two-way communication with a plurality of sensors, each of the plurality of sensors having its own channel. An electronic signal receiver receives electronic signals from one or more of the plurality of sensors at a pre-defined sample rate. A signal combiner bundles the electronic signals from one or more of the plurality of sensors into a single electronic signal. A single channel output is used to provide the single electronic signal to the sensor event assessor.

Abstract: A sensor power management arrangement includes a signal processing circuit configured to receive signal from a sensor, to test the signal against at least one criterion, and to pass the signal for further processing in response to the signal passing the at least one criterion. In this way, only signals that are of a sufficient importance or significance will consume the maximum amount of processing energy and through processing by later processes or circuitry. Should a signal from a sensor not be strong enough or meet other criteria, power will not be wasted in preparing that signal for provision to the microcontroller or microprocessor. Additional flexibility in the sensor power management can be realized by adjusting the criteria against which the sensor signal is compared based on a status of the sensor apparatus.

Abstract: A computing device can include a connector to connect with a removable storage device. A switch can control the connector to prevent in a first state and allow in a second state at least one of the writing and erasing of a removable storage device connected to the connector. The switch can be prevented from changing states when a component is in a first configuration. The state of the switch can be changeable when the component is in a second configuration. The component is operationally connected to the computing device in the first configuration, and the component is operationally disconnected from the computing device in the second configuration.

Abstract: A method includes receiving, at a node located in a structure, an indication of an evacuation condition. The structure includes a plurality of nodes in communication with one another. The method also includes sending, by the node, a message to one or more additional nodes. The message informs the one or more additional nodes that the node is going to determine an evacuation route in response to the indication of the evacuation condition such that the one or more additional nodes do not determine the evacuation route. The method also includes determining, by the node, the evacuation route based at least in part on the indication of the evacuation condition and at least in part on a layout of the structure. The method further includes providing, by the node, the evacuation route to the one or more additional nodes.

Abstract: The invention relates to a method for providing guaranteed quality of service in distributed computing platforms for execution of distributed applications, by combining: i) a partitioned operating system (POS) or a hypervisor (101) executed on at least two computers (300,301); where said POS/hypervisor allocates the CPU, memory and I/O hardware resources to computer partitions in said computers; where said computers are capable of executing different computer partitions (104, 105, 106) with different application tasks within one said computer partition or executing different operating systems (in case of hypervisor) within one said computer partition; wherein the said POS/hypervisor ensures that the application tasks executed in different partitions within the same said computer get their allocated hardware resources; wherein said POS/hypervisor performs a time-driven scheduling for a subset of computer partitions based on a given configuration (136), ii) means, for example network communication technology, f

Abstract: In one embodiment, a virtual room-based user interface includes one or more virtual rooms. Each virtual room is rendered from one or more images captured of a corresponding physical room of a structure, and includes depictions of one or more light fixtures within the physical room, one or more furnishings within the physical room and one or more boundaries of the physical room. A user selects a particular depiction of a particular light fixture within a particular virtual room. In response, a state of the particular light fixture within the corresponding physical room is changed. Also, appearance of the particular virtual room is updated such that the depiction of the particular light fixture shows the particular light fixture with the changed state and the depictions of the one or more boundaries or the one or more furnishings show lighting effects resulting from the changed state.

Abstract: An auto-powered mobile machine with controls for a riding operator and a system for carrying and making efficient use of a variety of attachable tools. Wireless radio communication from the controls to a lower tool may allow the swivel to spin any number of times without limitation. Hydraulic tool position controls are wirelessly coupled to a remote sensor that responds to a string datum line, a curb, direction of gravity, or GPS data.

Abstract: Embodiments of a solar powered energy module are provided wherein a solar powered module maybe added to a building or vehicle which is self-powered and need not be connected to the existing power system of the building or vehicle. The solar powered energy module may be utilized to power an awning or other desirable features.

Abstract: A method for controlling the fill volume of a grapple, such as a bulk-material crane grapple which includes at least one hoist-and-closure unit, may include adjusting the fill volume of the grapple is during the grapple closure process by adjusting/controlling the grapple hoist height. The grapple hoist speed and/or grapple hoist height may be the controlling parameter for the adjustment of the fill volume of the grapple.

Abstract: A fan control method, apparatus, and system, so as to implement speed regulation and rotation direction control on a four-wire system counter-rotating fan with a conventional four-wire fan interface by using a PWM control bus. The method provided by the embodiments of the present invention includes: receiving a first fan regulation and control signal sent by a system control module; converting the first fan regulation and control signal to a forward-rotating control signal, a counter-rotating control signal, or a rotation direction switchover control signal according to a duty cycle range of the first fan regulation and control signal and a current rotation direction of the fan; and sending a control signal obtained by the conversion to a fan driving module, so that the fan driving module drives, according to the control signal obtained by the conversion, the fan to operate.

Abstract: A building data managing apparatus according to an embodiment of present invention, includes a first processing unit for receiving from equipments within a building a first management data having BACnet protocol and a second management data having wireless communication protocol via the Ethernet communication interface, and converting the first management data and the second management data to BAS (Building Automation System) common communication layer data, a second processing unit for converting the BAS common communication layer data to commissioning common communication layer data, and a third processing unit for converting the commissioning common communication layer data to commissioning common communication layer message having protocol for transmission to an external control server.

Abstract: Current handheld marking devices typically use hand movement to create marks on a surface. Marks, in this context, can be defined as an area on a surface having different physical properties from its surroundings. Such marks are created by the motion of a marking region that travels on a surface plane, creating a mark over time. Examples of such devices are: pens, brushes, markers, spray tools, and engraving instruments. Marking devices carry motion from the brain, to the hand, through the device and onto the surface. A feedback loop is created from the brain to hands to a final mark on a surface. The mark is observed as it is created and loops back into the brain. This creative mark making loop is the process to generate a visual element or design on a surface. Typically this loop is consistent across handheld marking devices.

Abstract: A network system may be provided that includes an electronic product, a recognition target, a recognition device, a setting program and a display unit. The electronic product may operate to manage or process a target. The recognition target may include information relating to the target. The recognition device may recognize information listed on the recognition target. The setting program may convert information recognized by the recognition device into setting information. The display unit may display the setting information converted by the setting program.

Abstract: The invention relates to a machine component of a drive train and to a method for configuring and/or putting into operation and/or operating such a drive train (2) of a machine (1), which drive train comprises machine components that can be controlled by means of a control unit (9) as well as non-controllable machine components (5-8), wherein the method comprises the steps of: equipping at least a portion of the non-controllable machine components (5-8) with component-specific data storage devices (12-15), on which in each case design-related technical data of the non-controllable machine components (5-8) are stored, which data are relevant for the control of one or several controllable machine components (3-4); transmitting the data stored on the data storage devices (12-15) to the control unit (9); and controlling one or more controllable machine components (3, 4) by using the control unit (9) and on the basis of the data transmitted.

Abstract: An air conditioning management system manages air conditioning units having unique physical addresses using logical addresses. The system includes a local controller collecting driving information for the air conditioning units, and an operating unit for each air conditioning unit. The local controller has a memory section which stores identification information for each of the air conditioning units, an information collecting section which collects the driving information, and an associating section which associates the driving information with the logical addresses. The identification information for each of the air conditioning units has a physical address section, a real address section set from the operating unit, and a temporary address section arbitrarily settable without the operating unit. The associating section uses the real address as the logical address when the real address is set and uses the temporary address as the logical address when the real address is not set.

Abstract: The present invention relates to a control system for operating a crane (101). The control system includes a central control module (125) for controlling operation of the crane (101) and a control unit (121) for outputting control signals to the central control module in response to user inputs. At least one portable safety unit (149) having a wireless transmitter for communicating with the central control module (125). The at least one portable safety unit (149) is provided with a safety module which is connected to the wireless transmitter. The safety module can be operated to transmit an inhibit signal wirelessly to the central control module (125) to inhibit operation of the crane (101). The present invention also relates to a crane (101) and a method of operating a crane (101).

Abstract: A component control system includes a component. At least one component element is included in the component. A component controller is included in the component, coupled to the at least one component element, and operable to couple to an Information Handling System (IHS) controller. The component controller is operable to receive a normalized component performance (NCP) value from the IHS controller. The NCP value is associated with at least one component output range. The component controller is also operable to provide a control signal that is associated with the NCP value to the at least one component element. In response to receiving the control signal, the at least one component element operates such that the component produces at least one component output, and each component output produced by the component is within a corresponding component output range.

Abstract: A system which controls a group of multiple arrays of actuator elements, each of the actuator elements including a moving element which moves between a first and a second extreme positions; the system including: a controller, configured to generate control commands for at least one array of the multiple arrays in each individual cycle out of a series of sampling cycles, based on obtained information; and (b) an interface configured to transfer the control commands to the at least one array, thereby resulting in releasing from the first extreme position during the intended cycle of at least one moving element that is included in the at least one array; wherein release of all moving elements of at least one restrained array out of the multiple arrays is prevented during the intended cycle.

Abstract: A method and apparatus are disclosed for retrofitting a pedestal crane, the method comprising removing an existing motor generator controller for a motor in the pedestal crane; and replacing the motor generator controller with a digital controller.

Abstract: A controller (10) for a machine tool (18) for tapping by a main shaft and a feed shaft, comprising an identifier unit (12) for identifying an index of the size of the tap, a temperature detector unit (19b) for detecting the temperature of a motor (19a) for the main shaft, an acceleration storage unit (21) for storing the acceleration of the main shaft corresponding to the index of the size of the tap, a rate storage unit (22) for storing the rate of varying the acceleration of the main shaft depending upon the temperature of the motor, and an acceleration calculation unit (16) for calculating a new acceleration of the main shaft by multiplying an acceleration determined from the index of the size of the tap and from the acceleration storage unit by a rate determined from the detected temperature and from the rate storage unit.

Abstract: A method for predefining an operating point of a drive machine of a drive system, including the drive machine and at least two loads which are driven by the drive machine is disclosed. The method includes the following steps: (i) identification of in each case one instantaneous load power demand of the at least two loads, (ii) determination of at least one partial request point of the drive machine for each identified load power demand in order to meet the respective load power demand, (iii) determination of at least one overall request point of the drive machine on the basis of the specific partial request points, (iv) determination of a cost variable of the drive machine for the at least one overall request point, and (v) selection of the operating point taking into account the cost variable and predefining of the operating point.

Abstract: A powertrain system including a multi-mode transmission is configured to transfer torque among an input member, torque machines and an output member. A method for controlling the multi-mode transmission includes employing a closed-loop speed control system to determine torque commands for physical torque actuators including the torque machines. The closed-loop speed control system includes employing a virtual torque actuator control scheme to generate torque commands for the physical torque actuators responsive to output commands for a plurality of virtual torque actuators.

Abstract: In embodiments of electronic compensated pivot control, a computing device includes a device housing that is integrated with a display device, and the device housing tilts for multiple display positions. Pivotable components pivot in coordination to position the device housing in a display position, and sensors detect positioning inputs that are received to re-position the device housing of the computing device. Actuators are implemented for electronic actuation to limit movement of the pivotable components, and alternatively, to drive the pivotable components to re-position the device housing. A pivot controller is implemented to control the actuators based on sensor data to position the device housing in a display position.

Abstract: Methods and systems for determining states of environments and modifying the environments according to the states are disclosed. In one aspect, the method includes a robot device determining for an environment a state comprising a plurality of state attributes for the environment. The method further includes receiving a request for the state and, in response to receiving the request, modifying the environment to comprise at least some of state attributes. The robot device may determine the state by receiving indications of at least some of the state attributes from some or all of a user, a server, another robot device, and another device. The attributes may be user attributes for a particular user, or may be event attributes for a particular type of event. The request may take the form of a request from a user, a calendar event, or a user arrival.

Abstract: Systems and methods for determining operating settings for a fluid production system that includes wells and a processing facility, the method including identifying at least one swing well and one or more non-swing wells and determining at least one target parameter equation that is a function of at least one processing facility constraint and one or more non-swing well parameters. The method further includes incorporating the target parameter equation into a fully-coupled equation set representing the production system, simulating the production system using the fully-coupled equation set to obtain one or more operating settings that meet the processing facility constraint, and presenting to a user the operating settings.

Abstract: The present invention provides a method and device for remotely controlling a household appliance. The method includes: sending, by a social application client, a control command for a target household appliance, wherein the control command includes an account of the target household appliance, and the account of the target household appliance is a unique social account registered in a social application server when the target household appliance leaves a factory; and controlling, by the social application client, the target household appliance corresponding to the account of the target household appliance according to the control command. The present invention enables a user to directly control the household appliance through the social application client, thus improving the efficiency of controlling the household appliance and reducing the cost.

Abstract: A pool or spa control system includes, a main control panel housing a motherboard, relay bank, and local terminal. The motherboard includes a processor in two-way communication with a relay bank socket via an internal bus. The relay bank is connectable to the relay bank socket and includes a processor, memory, plurality of relays, connector, and an internal bus establishing two-way communication between the relay bank processor and the motherboard processor when the relay bank is connected to the relay bank socket. The local terminal includes a control processor, user interface, and memory, and is in two-way communication with the motherboard processor for allowing user control of the system. The control processor automatically discovers and assigns the relay bank a network address upon connection of the relay bank to the motherboard relay bank socket, and the relay bank returns relay bank parameter information, which the local terminal stores in memory.

Abstract: A system that allows a contractor to remotely monitor and/or interact with its customers' building control systems, such as heating, ventilating and air conditioning (HVAC) systems, and analyze information obtained from the building control systems over time. Such a system may help the contractor monitor and diagnosis customer building control systems, setup service calls, achieve better customer relations, create more effective marketing opportunities, as well as other functions. In some cases, the disclosed system may be configured to allow a user to grant or deny access to its HVAC system in response to the user receiving an electronic invitation to the system. The granting of access by a user to its HVAC system may allow for remote monitoring of the HVAC system.

Abstract: A system that allows a contractor to remotely monitor and/or interact with its customers' building control systems, such as heating, ventilating and air conditioning (HVAC) systems, and analyze information obtained from the building control systems over time. Such a system may help the contractor monitor and diagnosis customer building control systems, setup service calls, achieve better customer relations, create more effective marketing opportunities, as well as other functions. In some cases, the disclosed system may include a controller that analyzes data from HVAC systems, determines if one or more of the HVAC systems may benefit from a particular product or service, and outputs the HVAC systems that are determined to benefit from a particular product or service.

Abstract: A performance management system, method and a non-transitory computer readable storage medium are disclosed herein. The performance management system includes a value-driven management module and an integrated control module. The value-driven management module includes a value-driven model configuration unit and a value-driven target configuration unit. The value-driven model configuration unit is configured to configure a value-driven model with a plurality of targets, and the targets respond to a plurality of factors. The value-driven target configuration unit is configured to set a goal value for each of the targets. The integrated control module is configured to monitor a performance of a building in accordance with the goal value for each of the targets and the value-driven model.

Abstract: A system allows a contractor to remotely monitor and/or interact with its customers' building control systems, such as heating, ventilating and air conditioning (HVAC) systems, and analyze information obtained from the building control systems over time. Such a system may help the contractor monitor and diagnosis customer building control systems, setup service calls, achieve better customer relations, create more effective marketing opportunities, as well as other functions. In some cases, the disclosed system may include a controller that outputs a listing of one or more building automation system contractors having a service area that overlaps a geographical location of a customer or a potential customer or of a related HVAC system. In some cases, the disclosed system may output a listing of one or more building automation system contractors having a service area that overlaps a geographical location of a building automation system for which an alert has been indicated.

Abstract: A system that allows a contractor to remotely monitor and/or interact with its customers' building control systems, such as heating, ventilating and air conditioning (HVAC) systems, and analyze information obtained from the building control systems over time. Such a system may help the contractor monitor and diagnosis customer building control systems, setup service calls, achieve better customer relations, create more effective marketing opportunities, as well as other functions. In some cases, the disclosed system may help a contractor pro-actively identify possible issues with its customer's building control systems. A controller of the system may populate a display screen on a remote device to display a summary display screen with selectable features for obtaining detailed information related to the selected feature. The summary display screen may display a summary of business performance data, customer performance data, and/or HVAC performance data associated with a set of log-in credentials.

Abstract: A building controller for controlling one or more building control components in a building, wherein the building controller is configured for bidirectional communication via a communication network between the building controller and the one or more building control components. The building controller can include a housing, a control unit, and a display unit. The control unit can execute an operating system and a building control application program having a control algorithm. The display unit may be configured to display at least one screen that facilitates user monitoring of diagnostic messages of the operating system of the control unit. Alternatively, or in addition, the display unit can be configured to display a screen to facilitate user entry of operating system parameters and/or a screen to facilitate entry of operating system commands for execution on by the control unit.

Abstract: A motor controller including a communication port and a computing device coupled to the communication port is described. The computing device is capable of communicating using a plurality of communication protocols and is configured to detect that an external device has connected to the communication port. The computing device is further configured to identify a first communication protocol used by the external device, wherein the first communication protocol is one of the plurality of communication protocols, and communicate with the external device using the first communication protocol.

Abstract: A servo transfer press system generates a press phase signal and a transfer phase signal that are synchronized with a master phase signal, performs a press operation according to a reference press motion based on the press phase signal, and performs a transfer operation according to a reference transfer motion based on the transfer phase signal. The servo transfer press system includes a reference interference diagram generation section, a reference interference diagram storage section, an operation interference diagram generation section, an interference presence/absence comparison-determination section, and a phase signal relative relationship adjustment section, and performs a transfer press operation while avoiding interference by performing an automatic phase signal adjustment when a motion has been changed.

Abstract: A method of facilitating a drilling operation includes: receiving a current set point for a drilling operation, the current set point indicating a value of an operational parameter at which the drilling operation is being performed; receiving a global limit indicating at least one of a maximum and a minimum value of the operational parameter that is permitted to be applied for the drilling operation; defining a local limit for the operational parameter, the local limit indicating at least one of a local maximum value and a local minimum value of the operational parameter; receiving a parameter change value, the parameter change value indicating a proposed change to the operational parameter from the current set point; and selecting a level of automation by which the operational parameter can be adjusted, the level of automation based on a comparison of the parameter change value and the local limit.

Abstract: A method and apparatus for estimating the instantaneous rotational speed of a bottom hole assembly at the lower end of a drill string. In one embodiment, a method includes driving the drill string by a drilling mechanism at the upper end of the drill string. A fundamental frequency of stick-slip oscillations suffered by the drill string is estimated. Variations in a drive torque of the drilling mechanism are determined. Known torsional compliance of the drill string is combined with the variations in the drive torque. An output signal representing the instantaneous rotational speed is provided.