13.4 Equations of Motion

This section shows how to access the complete system of equations that is generated by a Mech model.

13.4.1 Internal Expression Access

The following functions are used to access the symbolic expressions that are generated by MechanicalSystems.

Functions to provide access to internally stored expressions.

Functions that return a model's dependent variables.

In all of these functions, the body number bnum can be a single positive integer, a list of integers, All, or Rest. The constraint number cnum can be a single positive integer constraint number, a list of integers, All, Euler, or any of the forms of partial constraint specifications accepted by Constraints.
The complete set of equations that are solved by the Static solution block is given by Transpose[Jacobian[_,_]].Generalized[_] Loads[_]. The equations of motion that are solved by the Dynamic solution block are the Static equations with Centrifugal[_] + MassMatrix[_].Acceleration[_] added to the left-hand side.

13.4.2 Examples

Here is a simple model to provide some values for the dependent variables.

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The model is run with the Dynamic solution option, and very tight convergence criteria.

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Here are all the kinematic constraint equations.

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Here are the velocity constraints.

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Here are the acceleration constraints.

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Here are the static reaction force equations. They are not satisfied because the model was solved with the Dynamic option.

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Here are the dynamic equations of motion.

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