Providing a unique bridge between the foundations of analytical mechanics and application to multi-body dynamical systems, this textbook is particularly well suited for graduate students seeking an understanding of the theoretical underpinnings of analytical mechanics, as well as modern task space approaches for representing the resulting dynamics that can be exploited for real-world problems in areas such as biomechanics and robotics. Established principles in mechanics are presented in a thorough and modern way. The chapters build up from general mathematical foundations, an extensive treatment of kinematics, and then to a rigorous treatment of conservation and variational principles in mechanics. Parallels are drawn between the different approaches, providing the reader with insights that unify his or her understanding of analytical dynamics. Additionally, a unique treatment is presented on task space dynamical formulations that map traditional configuration space representations into more intuitive geometric spaces.
Author(s): Vincent De Sapio
Publisher: Cambridge University Press
Year: 2017
Language: English
Pages: 305
Contents......Page 6
Illustrations......Page 7
Tables......Page 12
Preface......Page 13
Notation......Page 18
1.1 Historical Background......Page 24
1.2 Devices That Illustrate Principles of Analytical Dynamics......Page 28
1.3 Scope of This Book......Page 31
2.1 Linear Systems......Page 33
2.2 Differential Geometry......Page 46
2.3 Optimization......Page 51
2.4 Exercises......Page 54
3.1 Spherical Kinematics......Page 59
3.2 Spatial Kinematics......Page 77
3.3 Kinematic Chains......Page 92
3.4 Kinematic Constraints and Degrees of Freedom......Page 99
3.5 Exercises......Page 100
4.1 The Newton-Euler Principle......Page 106
4.2 Exercises......Page 122
5.2 D’Alembert’s Principle of Virtual Work......Page 124
5.3 Hamilton’s Principle of Least Action......Page 151
5.4 Canonical Hamiltonian Formulation......Page 165
5.5 Elimination of Multipliers......Page 168
5.6 Exercises......Page 170
6.2 Jourdain’s Principle of Virtual Power......Page 174
6.3 Kane’s Formulation......Page 202
6.4 Exercises......Page 208
7.2 Gauss’s Principle......Page 211
7.3 Gauss’s Principle of Least Constraint......Page 224
7.4 Gibbs-Appell Formulation......Page 229
7.5 Exercises......Page 234
8.1 Task Space Framework......Page 237
8.2 Constrained Dynamics in Task Space......Page 250
8.3 Exercises......Page 256
9.1 Musculoskeletal and Neuromuscular Dynamics......Page 258
9.2 Constrained Dynamics of Biomechanical Systems......Page 268
10.1 General Purpose Mathematical Software......Page 286
10.2 Dedicated Multibody Dynamics Software......Page 291
A.1 Continuum Kinematics......Page 292
A.2 Continuum Dynamics......Page 293
A.3 Subsystem Assembly......Page 296
References......Page 298
Index......Page 302
