10.1.2 Finding Equilibrium

To find the equilibrium configuration of a mechanism, a FreeSystem object is built that contains a new set of equations of motion with one or more constraints removed from the model.

Finding equilibrium configuration.

The pendulum-on-a-rope model has three constraints that are present only to complete the kinematic model, constraints 5, 6, and 7. Each of these constraints is dropped, one at a time, and the equilibrium position is found with each new degree of freedom. The first constraint to be dropped is constraint 7, which locks the rotation of the pendulum relative to the slider. This allows the pendulum to rotate, but the slider stays locked at the center of the rope.

This drops constraint 7.

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This solves the FreeSystem object.

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Here is the pendulum model with constraint 7 dropped.

Next, constraint 5 is dropped, allowing the slider to move along the rope. Finally, constraint 6 is dropped, allowing the slider to rotate. The InitialGuess option is used to pass SetFree the solution to the last FreeSystem, which is named sol. This solution is a better initial guess than the defaults pulled from LastSolve[].

An option for SetFree.

Here is another FreeSystem object with constraints 5 and 7 dropped.

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This solves the FreeSystem object. Note that X2 has increased because the slider has moved to the right.

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Here is the equilibrium position with constraints 5 and 7 dropped.

Here a FreeSystem object with constraints 5, 6, and 7 dropped is built and solved.

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Here is the complete equilibrium position of the pendulum-on-a-rope model.

This returns MechanicalSystems to its initial state.

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