10.3.4 Instantaneous Free Acceleration

To find the free acceleration of the gyroscope, one or more constraints must be dropped. The constraint that prevents rotation of the base, constraint 2, is dropped first. The rotor cannot precess in this state because the gimbal is still locked to the base, but the reaction torques applied to the base that accelerate the rotor can be measured.
No initial conditions are explicitly given. Initial guesses are taken from the default initial guesses that were set by the last run of SolveMech.

This drops the constraint that locks the base relative to the ground.

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This solves the FreeSystem object.

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The angular acceleration of the rotor is 1.0 in the Z direction. This corresponds to the 1.0 applied moment divided by the 1.0 moment of inertia about the Z axis.

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There is no gyroscopic torque applied to the base by the Revolute5 constraint because the base has zero angular velocity at this instant.

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To make this model a little more interesting, the base is given a nonzero angular velocity with the InitialCondition option for SolveFree. This induces gyroscopic torques in the base constraint. To be consistent with the constraints the Z components of the initial angular velocity of each body must be identical.

This solves the FreeSystem object with a new partial initial condition. The rest of the initial conditions are taken from LastSolve[].

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The angular acceleration of the rotor now has a component in the Y direction corresponding to the changing direction of the angular velocity vector.

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Now there is a gyroscopic torque applied to the base by the Revolute5 constraint.

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Now the FreeSystem is rebuilt with both the base and the gimbal unlocked. The same initial velocity for the base, gimbal, and rotor is used so that the gyroscope precesses.

This builds and solves the FreeSystem object with constraints 2 and 4 dropped.

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Without the constraint forces applied by constraint 4, the gimbal has an angular acceleration about its Y axis induced by the gyroscopic forces.

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Again, there is no gyroscopic torque applied to the base by the Revolute5 constraint because the gimbal is free to rotate.

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