Dynamics: Theory and Application of Kane's Method

Abstract

Kane's method is a well-established approach to the formulation of the equations of motions of complex multibody mechanical systems. This method is systematic and clearly presented in the now famous book, Dynamics: Theory and Applications, by Kane and Levinson [1]. The present book, Dynamics: Theory and Application of Kane's Method, borrows material mostly from the original book of Kane and Levinson [1] and to a lesser extent, from the book, Spacecraft Dynamics, by Kane et al. [2]. New material and minor revisions contributed by Roithmayr and Hodges are distributed throughout the text. The book is a timely and welcome update of the work of Kane and Levinson, provides coverage of a broader class of problems, and presents recent advances in the field.The book's layout follows closely that of the original work of Kane and Levinson. Special emphasis is given to the topic of constraints because classical approaches and Kane's method treat this topic differently. Furthermore, the treatment of motion constraints has been expanded to focus on the forces and torques required to enforce such constraints exactly. The chapter dealing with the extraction of information from the equation of motion has also been augmented to include the checking function, which can be constructed even when an energy integral does not exist. The material presented in the last chapter, which deals with the manipulation of finite rotation, is largely drawn from the book Spacecraft Dynamics [2] with the exception of the first two sections that present the Wiener-Milenković parameters.This book covers material presented in graduate-level courses in physics or mechanical and aerospace engineering. A typical course could be either a first-year graduate course in dynamics or a follow-up course, if the first-year introductory course is based on the classical treatment of dynamics. The coverage focuses on rigid multibody systems, such as spacecraft, robotic manipulators, or articulated mechanisms. From the onset of the presentation, a specific notation is introduced that emphasizes frames of reference, regarded as massless rigid bodies. Constraints are introduced early on: both holonomic and nonholonomic constraints are treated in a unified manner. Rather than enforcing constraints via the classical Lagrange multiplier technique, Kane's equations are used as the basis of the formulation.The book addresses the relevant topics in a sequential manner. After a review of basic calculus techniques in the first chapter, the kinematics of rigid bodies is presented, followed by the discussion of configuration and motion constraints. Mass distribution and generalized forces are presented next. Constraint forces and torques are discussed in an independent chapter. After a discussion of energy functions, the derivation of the equations of motion is presented, and the procedures for extracting information from these equations of motion are developed. The final chapter of the book is devoted to the representation of finite rotation.Over one-quarter of the book is devo...

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Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

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“…Mechanical motion of mass in six degrees of freedom is completely described by separate treatment of three degrees of freedom of translation plus three additional degrees of freedom of rotation as articulated in the year 1830 [1] and expanded and modernized over the following two centuries [2][3][4][5][6][7][8][9][10][11][12][13]. Translational degrees of freedom are governed by Newton's law, while rotational degrees of freedom behave in accordance with Euler's law.…”