Motion of a rigid body in Abaqus/Standard

This problem illustrates the accuracy of the integration of rotations during implicit dynamic calculations on a rotating body whose rotary inertia is different in different directions.

The following topics are discussed:

Related Topics
In Other Guides
Implicit dynamic analysis
Rotary inertia element

ProductsAbaqus/Standard

We consider two cases of rigid body dynamics:

  • force-free motion of a rigid body; and

  • forced motion of a rigid body.

The Euler's equations for the motion of a rigid body in a rotating coordinate system attached to the body are

I11ϕ¨1+(I33-I22)ϕ˙2ϕ˙3=N1,I22ϕ¨2+(I11-I33)ϕ˙3ϕ˙1=N2,I33ϕ¨3+(I22-I11)ϕ˙1ϕ˙2=N3.

In these relations ϕ˙ is the body's angular velocity; ϕ¨ is its angular acceleration; I11,I22,I33 are the second moments of inertia along the principal axes of the body; and N1,N2,N3 are the torque components acting on the rigid body.