A Generalization of the Bresse Properties in Higher-Order Kinematics

This paper proposes a novel analysis method for higher-order acceleration vector fields in the case of rigid body planar motion, using the property of isomorphism with rotation group of planar motion and the group of unit algebra of the complex number. The equations that allow the determination of higher-order accelerations and his properties field are given. A generalization for high order classical Bresse circles is presented for the first time. The results are in closed form and coordinate-free. As a case, the velocities, accelerations, jerks, and jounces fields are offered for a general kinematic. This paper proposes a novel analysis method for higher-order acceleration vector fields in the case of rigid body planar motion, using the property of isomorphism with the rotation group of planar motion and the group of the unit algebra of the complex number. The equations that determine higher-order accelerations and their properties field are given. A generalization for high-order classical Bresse circles is presented for the first time. The results are in closed form and coordinate-free. As a case, the velocities, accelerations, jerks, and jounces fields are offered for a general kinematic.