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3.11 Rigid Section
The Rigid section is used to define all rigid constraints, rigid body initial kinematics, and rigid connectors. The motion of a point connected to a rigid body is given by where is the position of the rigid body center of mass and is the body's (proper orthogonal) rotation tensor, which satisfies at the initial time ; here, is the position vector of the point relative to the body's center of mass, and is the initial position. In FEBio, the rotation is evaluated as , where is the material rotation of the rigid body from its reference configuration. In practice, is stored as a quaternion to facilitate the multiplication of rotation tensors. The exponential map is given in full form as where is the third-order permutation pseudo-tensor with rectangular components (permutation symbol). Here, is the unit vector along the axis of rotation and is the angle of rotation about , such that . Both and may evolve over time. Either none or all the components of must be prescribed (or fixed) for a rigid body.