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MotionSolve Reference Guide
This manual provides a detailed list and usage information regarding command statements, model statements, functions and the Subroutine Interface available in MotionSolve.
Functions
WDTM
The WDTM function computes the magnitude of the total relative rotational acceleration between markers I and J. Time derivatives are calculated in the reference frame of marker L. The first argument, marker I, must be specified.

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MotionSolve is a system level, multibody solver that is based on the principles of mechanics.
MotionSolve Reference Guide
This manual provides a detailed list and usage information regarding command statements, model statements, functions and the Subroutine Interface available in MotionSolve.
- Notation and Syntax
- Creating MotionSolve XML Files
- Writing Custom Elements for MotionSolve
- Writing Custom Functions for MotionSolve
- Supported Versions - Third Party Software
- Command Statements
- Model Statements
- Functions
  - ABS
    Returns the absolute value of function expression x.
  - ACCM
    The ACCM function computes the magnitude of the total relative translational acceleration between markers I and J.
  - ACCX
    The ACCX function computes the X-component of the relative translational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - ACCY
    The ACCY function computes the Y-component of the relative translational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - ACCZ
    The ACCZ function computes the Z-component of the relative translational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - ACOS
    Returns the arc cosine of expression x.
  - AINT
    Returns the nearest integer whose value is not greater than the integral value of x.
  - AKISPL
    Returns the interpolated value or n-th derivative of the interpolated value of Reference_Spline element.
  - ANINT
    Returns the nearest integer to x.
  - ARYVAL
    Returns the specified component of the Reference_Array element.
  - ASIN
    Returns the arc sine of expression x.
  - ATAN
    Returns the arc tangent of expression x.
  - ATAN2
    Returns the arc tangent of expression y/x.
  - AX
    The AX function computes the relative rotational displacement of marker I with respect to marker J about the X-axis of marker J.
  - AXU
    This is the same as AX, but returns an unwrapped angle. Refer to the AX help page.
  - AY
    The AY function computes the relative rotational displacement of marker I with respect to marker J about the Y-axis of marker J.
  - AYU
    This is the same as AY, but returns unwrapped angle. Refer to the AY help page.
  - AZ
    The AZ function computes the relative rotational displacement of marker I with respect to marker J about the Z-axis of marker J.
  - AZU
    This is the same as AZ, but returns unwrapped angle. Refer to the AZ help page.
  - BEAM
    Returns force component due to Force_Beam element in reference frame of marker RM.
  - BISTOP
    The BISTOP function models a gap element.
  - BUSH
    This function returns the specified component of a force in a bushing element.
  - CHEBY
    The Cheby function evaluates a Chebyshev polynomial at a specific value $x$ .
  - CONTACT
    The CONTACT function returns a scalar result associated with a Force_Contact element.
  - COS
    Returns the cosine of expression x.
  - COSH
    Returns the hyperbolic cosine of expression x.
  - COUPLER
    Returns force component due to Constraint_Coupler element in reference frame of marker RM.
  - CUBSPL
    Returns the interpolated value or n-th derivative of the interpolated value of Reference_Spline element.
  - CURVE
    Evaluates a Reference_ParamCurve element at a specified location.
  - CVCV
    Returns force component due to CVCV element in reference frame of marker RM.
  - CVSF
    Returns force component due to Constraint_CVSF element in reference frame of marker RM. jflag indicates whether force acting on I or J marker is desired.
  - DELAY
    The DELAY function computes the value of an expression specified by val at a delayed time.
  - DIF
    Returns the value of the state variable defined by the Control_Diff element.
  - DIF1
    Returns the time derivative of the state variable defined by the Control_Diff element.
  - DIM
    The DIM function computes the positive difference of two expressions, e1 and e2, as follows: DIM(e1, e2) = max { 0, e1-e2 }
  - DM
    The DM function computes the magnitude of the total relative translational displacement between two markers.
  - DTOR
    Returns the factor for converting from degrees to radians.
  - DX
    The DX function computes the X-component of the relative translational displacement of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - DY
    The DY function computes the Y-component of the relative translational displacement of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - DZ
    The DZ function computes the Z-component of the relative translational displacement of marker I with respect to marker J, as resolved in the coordinate system of marker K.
  - EXP
    Returns the value $e^{x}$ .
  - FIELD
    Returns force component due to Force_Field element in reference frame of marker RM.
  - FITSPL
    Returns the interpolated value or n-th derivative of the interpolated value of the Reference_Spline element.
  - FM
    The FM function computes the magnitude of the resultant translational force acting at marker I (obtained by vector summation), due to all applied forces and constraints that act between marker I and marker J.
  - FORCOS
    The Forcos function evaluates a Fourier Cosine series at a specific value $x$ .
  - FORSIN
    The FORSIN function evaluates a Fourier sine series at a specific value $x$ .
  - FRICTION
    The FRICTION function computes the output of a Force_JointFriction corresponding to the ID and the component index specified in comp.
  - FX
    The FX function computes the X-component of the resultant translational force acting at marker I (obtained by vector summation), due to all applied forces and constraints that act between markers I and J, as resolved in the coordinate system of marker K.
  - FXFREQ
    Returns the frequency in cycles per time-unit for the current mode.
  - FXMODE
    Returns the mode number of the current mode of the flexible body.
  - FY
    The FY function computes the Y-component of the resultant translational force acting at marker I (obtained by vector summation), due to all applied forces and constraints that act between markers I and J, as resolved in the coordinate system of marker K.
  - FZ
    The FZ function computes the Z-component of the resultant translational force acting at marker I (obtained by vector summation), due to all applied forces and constraints that act between markers I and J, as resolved in the coordinate system of marker K.
  - GFORCE
    This function returns the specified component of the force and/or torque applied by the Force_Vector_TwoBody or Force_Vector_OneBody element.
  - HAVSIN
    Given a specific $x$ value, the Havsin function evaluates the $y$ value of a Haversine function that smoothly transitions from $(x_{0}, y_{0})$ to $(x_{1}, y_{1})$ .
  - IF
    The IF function can be used to define a conditional expression.
  - IMPACT
    The IMPACT function models impact forces acting on bodies during collision. The elastic properties of the boundary surface between the two bodies can be tuned as desired.
  - INCANG
    Returns the included angle defined using three markers: I,J, K. Angle between the line connecting I with J and the line connecting J with K is reported. As the simulation proceeds, the first non-zero value is always positive.
  - JOINT
    This function returns the specified component of the force or torque due to the Constraint_Joint element.
  - JPRIM
    Returns constraint force component comp associated with Constraint_Jprim with the ID "id", calculated in the reference frame of marker "RM".
  - KE
    Returns the kinetic energy of a rigid or flexible body.
  - LINSPL
    Returns the interpolated value or n-th derivative of the interpolated value of Reference_Spline element.
  - LOG
    Returns the natural logarithm of x. For example, if x = $e^{a}$ , then log(x) = a. The log function is defined only for x > 0; it is undefined for all other values.
  - LOG10
    Returns the logarithm of x to the base 10. For example, if x = $10^{a}$ , then LOG10(x) = a. The log function is defined only for x > 0; it is undefined for all other values.
  - MATE
    Returns constraint force component comp, associated with Constraint_Mate with the ID id, calculated in the reference frame of marker RM.
  - MAX
    Returns the maximum of two expressions num1 and num2.
  - MIN
    Returns the minimum of two expressions num1 and num2.
  - MOD
    The MOD function returns the remainder when a is divided by b, MOD(a,b) = a - int(a/b) * b.
  - MODE
    Returns the current analysis mode.
  - MOTION
    This function returns the specified component of the force or torque due to the Motion_Joint or Motion_Marker element.
  - NFORCE
    Returns force component "comp" acting on marker "i" due to Force_MultiPoint element with ID "id", in reference frame of marker "RM".
  - PHI
    The PHI function computes the third angle, in radians, of a body-2 Euler angle rotation sequence (body-3, body-1, body-3) of marker I with respect to marker J.
  - PI
    Returns the value of PI (π).
  - PINVAL
    Returns a specific component of the Control_PlantInput element.
  - PITCH
    The PITCH function computes the second angle, in radians, of a body-3 Yaw-Pitch-Roll rotation sequence.
  - POLY
    The POLY function evaluates a standard polynomial at a specific value $x$ .
  - POUVAL
    Returns a specific component of Control_PlantOutput element.
  - PROXIMITY
    Returns the components of the proximity sensor.
  - PSI
    The PSI function computes the first angle, in radians, of a body-2 Euler angle rotation sequence (body-3, body-1, body-3) of marker I with respect to marker J.
  - PTCV
    Returns force component due to Constraint_PTCV element in reference frame of marker RM. v indicates whether the force acting on the I or J marker is desired.
  - PTSF
    Returns force component due to Constraint_PTSF element in reference frame of marker RM. jflag indicates whether force acting on I or J marker is desired.
  - Q
    The Q()function returns the modal displacement for the requested mode (m_id) for the flexible body specified (f_id). This function can be used in your model as a valid MotionSolve expression.
  - QDDOT
    The QDDOT() function returns the modal acceleration for the requested mode (m_id) for the flexible body specified (f_id). This function can be used in your model as a valid MotionSolve expression.
  - QDOT
    The QDOT() function returns the modal velocity for the requested mode (m_id) for the flexible body specified (f_id). This function can be used in your model as a valid MotionSolve expression.
  - QUISPL
    Returns the interpolated value or n-th derivative of the interpolated value of the Reference_Spline element.
  - ROLL
    The ROLL function computes the third angle, in radians, of a body-3 Yaw-Pitch-Roll rotation sequence.
  - RTOD
    Returns the factor for converting from radians to degrees.
  - SENVAL
    Returns the last stored value from the Sensor_Evaluate element.
  - SFORCE
    This function returns the specified component of the force applied by the Force_Scalar_TwoBody element.
  - SFSF
    Returns force component due to Constraint_SFSF element in reference frame of marker RM. jflag indicates whether force acting on I or J marker is desired.
  - SHF
    The SHF function evaluates a simple harmonic function at a specific value $x$ .
  - SIGN
    The SIGN function transfers the sign of a2 to the magnitude of a1.
  - SIN
    Returns the sine of expression x.
  - SINH
    Returns the hyperbolic sine of expression x.
  - SPDP
    Returns a force component due to the Force_SpringDamper element in reference frame of marker RM. jflag indicates whether force acting on I or J marker is desired.
  - SQRT
    Returns the square root of x. The SQRT function is defined only for x >= 0; it is undefined for all other values.
  - STEP
    Given a specific $x$ value, the Step function evaluates the $y$ value of a function that smoothly transitions from $(x_{0}, y_{0})$ to $(x_{1}, y_{1})$ . This function has continuous first and second derivatives, but discontinuous third derivatives at the end points.
  - STEP5
    Given a specific $x$ value, the Step5 function evaluates the $y$ value of a function that smoothly transitions from $(x_{0}, y_{0})$ to $(x_{1}, y_{1})$ This function has continuous first and second derivatives, but discontinuous third derivatives at the end points.
  - SWEEP
    The SWEEP function evaluates a sinusoidal function that has constant amplitude but linearly increasing frequency at a specific $x$ value.
  - TAN
    Returns the tangent of expression x.
  - TANH
    Returns the hyperbolic tangent of expression x.
  - THETA
    The THETA function computes the second angle, in radians, of a body-2 Euler angle rotation sequence (body-3, body-1, body-3) of marker I with respect to marker J.
  - TIME
    The TIME variable returns the current simulation time.
  - TM
    The TM function computes the magnitude of the resultant torque acting at marker I (obtained by vector summation), due to all applied torques and constraints that act between marker I and marker J. Markers I and J must be specified.
  - TRIM
    The TRIM function smoothly interpolates between the slope m₁ defined through the line segment given by x0, y0, x1, y1 and m₂ defined through the line segment given by x1, y1, x2, y2.
  - TX
    The TX function computes the X-component of the resultant torque acting at marker I (obtained by vector summation), due to all applied torques and constraints that act between marker I and marker J, as resolved in the coordinate system of marker K.
  - TY
    The TY function computes the Y-component of the resultant torque acting at marker I (obtained by vector summation), due to all applied torques and constraints that act between markers I and J, as resolved in the coordinate system of marker K.
  - TZ
    The TZ function computes the Z-component of the resultant torque acting at marker I (obtained by vector summation), due to all applied torques and constraints that act between markers I and J, as resolved in the coordinate system of marker K.
  - VARVAL
    Returns current value of Reference_Variable element.
  - VFORCE
    This function returns the specified component of the force applied by the Force_Vector_TwoBody or Force_Vector_OneBody element.
  - VM
    The VM function computes the magnitude of the total relative translational velocity between markers I and J. Time derivatives are calculated in the reference frame of marker L. The first argument, marker I, must be specified. The second and third arguments are optional.
  - VR
    Returns the relative velocity of marker I with respect to J. Time derivatives are computed in the reference frame of marker L. Markers J and K are optional.
  - VTORQ
    This function returns the specified component of the torque applied by the Force_Vector_TwoBody or Force_Vector_OneBody element.
  - VX
    The VX function computes the X component of the relative translational velocity of marker I with respect to marker J resolved in the coordinate system of marker K. The time derivatives are taken in the marker L. Arguments J, K, and L are optional and default to 0, which refers to Global Frame.
  - VY
    The VY function computes the Y component of the relative translational velocity of marker I with respect to marker J resolved in the coordinate system of marker K. The time derivatives are taken in the marker L. Arguments J, K, and L are optional and default to 0, which refers to Global Frame.
  - VZ
    The VZ function computes the Z component of the relative translational velocity of marker I with respect to marker J resolved in the coordinate system of marker K. The time derivatives are taken in the marker L. Arguments J, K, and L are optional and default to 0, which refers to Global Frame.
  - WDTM
    The WDTM function computes the magnitude of the total relative rotational acceleration between markers I and J. Time derivatives are calculated in the reference frame of marker L. The first argument, marker I, must be specified.
  - WDTX
    The WDTX function computes the X-component of the relative rotational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K. The time derivatives are taken in the marker L frame. The first argument, marker I, must be specified.
  - WDTY
    The WDTY function computes the Y-component of the relative rotational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K. The time derivatives are taken in the marker L frame. The first argument, marker I, must be specified.
  - WDTZ
    The WDTZ function computes the Z-component of the relative rotational acceleration of marker I with respect to marker J, as resolved in the coordinate system of marker K. The time derivatives are taken in the marker L frame. The first argument, marker I, must be specified.
  - WX
    The WX function computes the X-component of the relative rotational velocity of marker I with respect to marker J, as resolved in the coordinate system of marker K. The first argument, marker I, must be specified. The second and third arguments, markers J and K, are optional.
  - WY
    The WY function computes the Y-component of the relative rotational velocity of marker I with respect to marker J, as resolved in the coordinate system of marker K. The first argument, marker I, must be specified. The second and third arguments, markers J and K, are optional.
  - WZ
    The WZ function computes the Z-component of the relative rotational velocity of marker I with respect to marker J, as resolved in the coordinate system of marker K. The first argument, marker I, must be specified. The second and third arguments, markers J and K, are optional.
  - YAW
    The YAW function computes the first angle, in radians, of a body-3 Yaw-Pitch-Roll rotation sequence.
  - YFORCE
    This function returns the specified component of the force applied by the Force_StateEqn element.
- The Subroutine Interface for MotionSolve
- ADM/ACF Entities
- NLFE Statements
- msolve API Statements

WDTM

The WDTM function computes the magnitude of the total relative rotational acceleration between markers I and J. Time derivatives are calculated in the reference frame of marker L. The first argument, marker I, must be specified.

Format

WDTM(I, J, L)

Arguments

I: The marker whose acceleration is to be computed.
J: The marker with respect to which the acceleration is to be computed. If omitted, it defaults to the ground coordinate system.
L: Time derivatives are taken in the coordinate system of this marker. If omitted, it defaults to the ground coordinate system.

Example

<Post_Request
     comment          = "WM-WDTM-HAVSIN-FORSIN-DIM-ACOS"
     id               = "3"
     type             = "EXPRESSION"
     expr1            = "NULL"
     expr2            = "WM(30102010)"
     expr3            = "WDTM(30102010)"
     expr4            = "HAVSIN(TIME,1.,0.,4.,1.)"
     expr5            = "NULL"
     expr6            = "FORSIN(TIME,0.1,6.28,0.1,0.2)"
     expr7            = "DIM(TIME,1.0)"
     expr8            = "ACOS(COS(TIME))"
/>