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Analytical Dynamics
Analytical Dynamics presents balanced coverage of dynamics problems and formulations. From the classical methods to the newer techniques used in today's complex and multibody environments, this text shows mechanics, beginning at the particle mechanics level. It then extends these concepts to systems of particles, rigid bodies (plane motion and 3D), and lightly flexible bodies. The cornerstone variational principles of mechanics are developed and applied to particles, rigid bodies, and deformable bodies. Students are exposed to a natural flow of the concepts used in dynamics. The text emphasizes both the derivation of the describing equations and the response. The describing equations are developed using force and moment balances, as well as variational principles. Different approaches of obtaining equations of motion are discussed and compared. The response is analyzed qualitatively and quantitatively. The nature of the motion is explored by means of energy and momentum concepts and stability, as well as motion integrals. Small motions around equilibrium are discussed, together with the response of linearized systems.
Chapter 1 Basic Principles 1
Chapter 2 Relative Motion 87
Chapter 3 Dynamics of A System of Particles 153
Chapter 4 Analytical Mechanics: Basic Concepts 215
Chapter 5 Analytical Mechanics: Additional Topics 273
Chapter 6 Rigid Body Geometry 323
Chapter 7 Rigid Body Kinematics 355
Chapter 8 Rigid Body Dynamics: Basic Concepts 421
Chapter 9 Dynamics of Rigid Bodies: Advanced Concepts 489
Chapter 10 Qualitative Analysis of Rigid Body Motion 547
Chapter 11 Dynamics of Lightly Flexible Bodies 591
Appendix A A Brief History of Dynamics 669
Appendix B Concepts from the Calculus of Variations 687
Appendix C Common Inertia Properties 701
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