Geometry of motion and nutation stability of free axisymmetric variable mass systems

• Published in: Nonlinear dynamics Vol. 94; no. 3; pp. 2205 - 2218
• Main Author: Nanjangud, Angadh
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2018; Springer Nature B.V
• Subjects: Angular speed; Automotive Engineering; Axisymmetric bodies; Classical Mechanics; Configurations; Coning motion; Control; Cylinders; Dynamical Systems; Engineering; Equations of motion; Euler angles; Exact solutions; Mechanical Engineering; Motion stability; Nonlinear differential equations; Nonlinear equations; Nutation; Original Paper; Rocket engines; Solid propellant rocket engines; Variable mass systems; Vibration; Classical mechanics; Spacecraft attitude dynamics; Mass variation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-018-4485-6

In classical mechanics, the ‘geometry of motion’ refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterizing nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors.