Suppose that a linear spring of stiffness K and un stretched length ³0 is attached to a point XA on a rigid body and the other end of the spring is attached to a fixed point O. The position vector of...

Suppose that a linear spring of stiffness K and un stretched length ³0 is attached to a point XA on a rigid body and the other end of the spring is attached to a fixed point O. The position vector of XA relative to the center of mass of the rigid body is

(a) With the assistance of a set of 3–1–3 Euler angles, show that

In this equation,

(b) With the assistance of a set of 3–1–3 Euler angles, show that the potential energy of the spring is

Where

(c) Describe two equivalent methods to find the conservative force F_con
acting at X¯ and the conservative moment M_con
associated with the spring.