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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
ATAN2
Returns the arc tangent of expression y/x.

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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

ATAN2

Returns the arc tangent of expression y/x.

Format

ATAN2(y,x)

Description

A T A N 2 (y, x) = {\begin{cases} A T A N (\frac{y}{x}) x > 0 \\ A T A N (\frac{y}{x}) + π y ³ 0, x < 0 \\ A T A N (\frac{y}{x}) - π y < 0, x < 0 \\ + \frac{π}{2} y > 0, x = 0 \\ - \frac{π}{2} y < 0, x = 0 \\ u n d e f i n e d y = 0, x = 0 \end{cases}}

Arguments

x: Any valid function expression.

Example

<Reference_Variable
     id                  = "1"
     label               = "ATAN2 Example"
     type                = "EXPRESSION"
     expr                = "ATAN2(AY(569,193),AX(569,193)"
/>