A Closed-Form Expression of the Instantaneous Rotational Lurch Index to Evaluate Its Numerical Approximation

The lurch index has recently been introduced in applied kinematics as an integral descriptor of the fluency of the motion of a rigid body in space. It may be defined in different versions, according to the component of motion under investigation. In the present paper, we analyze a rotational lurch index, which describes the fluency of the spin component of motion and whose value depends, through involved relations, on the dynamics of three canonical descriptors of the orientation of a rigid body in space. The aim of the present paper is to offer a closed-form expression of the instantaneous component of the rotational lurch, which leads to the namesake index upon integration and normalization. The closed form of the index is, then, used to evaluate its practical calculation, based on numerical approximations on a number of data sets.