Author | Rosenberg, Reinhardt M. author |
---|---|
Title | Analytical Dynamics of Discrete Systems [electronic resource] / by Reinhardt M. Rosenberg |
Imprint | Boston, MA : Springer US, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-8318-5 |
Descript | XVIII, 426 p. 1 illus. online resource |
1. Introduction -- 2. Dynamical Systems -- 2.1. Particles -- 2.2. Systems of Particles -- 2.3. Forces and Laws of Motion -- 2.4. Galilean Transformations -- 2.5. Arguments of the Forces -- 2.6. The Problems of Particle Mechanics -- 3. Representations of the Motion -- 3.1. The Configuration Space -- 3.2. The Event Space -- 3.3. The State Space -- 3.4. The State-Time Space -- 3.5. Notions on the Concept of Stability -- 3.6. Problems -- 4. Constraints -- 4.1. General Observations -- 4.2. Holonomic Constraints -- 4.3. Nonholonomic Constraints -- 4.4. The Pfaffian Forms -- 4.5. When is a System of Constraints Holonomic? -- 4.6. Accessibility (of the Configuration Space) -- 4.7. Problems -- 5. The Strictly Newtonian Mechanics Problem -- 5.1. General Remarks -- 5.2. The Given Quantities and Relations -- 5.3. The First Problem -- 5.4. The Second Problem -- 5.5. Other Problems -- 5.6. Concluding Remarks -- 6. Some Rigid Body Kinematics -- 6.1. The Rigid Body -- 6.2. Finite Rotation -- 6.3. The Direction Cosines -- 6.4. Orthogonal Transformations -- 6.5. The Matrix Notation -- 6.6. Properties of the Rotation Matrix -- 6.7. The Composition of Rotations -- 6.8. Applications -- 6.9. Problems -- 7. Some Rigid Body Kinetics -- 7.1. Introductory Remarks -- 7.2. The Inertial Parameters in Rotated Axes -- 7.3. Angular Momentum and Principal Axes -- 7.4. The Ellipsoids of Cauchy and Poinsot -- 7.5. The General Motion of Rigid Bodies -- 7.6. Problems -- 8. The Nature of Lagrangean Mechanics -- 8.1. General Remarks -- 8.2. The Generalizations by Lagrange -- 9. Virtual Displacement and Virtual Work -- 9.1. General Observations -- 9.2. Classification of Displacements -- 9.3. DโAlembertโs Principle -- 9.4. The Nature of the Forces of Constraint -- 9.5. The Virtual Velocity -- 9.6. The Variation -- 9.7. Possible Velocities and Accelerations -- 9.8. The Fundamental Equation -- 9.9. The Nature of the Given Forces -- 9.10. Given Forces Which Are Functions of Constraint Forces -- 9.11. Problems -- 10. Hamiltonโs Principle -- 10.1. The Kinetic Energy -- 10.2. Kinetic Energy in Catastatic Systems -- 10.3. The Energy Relations in Catastatic Systems -- 10.4. The Central Principle -- 10.5. The Principle of Hamilton -- 10.6. Noncontemporaneous Variations -- 10.7. Lagrangeโs Principle of Least Action -- 10.8. Jacobiโs Principle of Least Action -- 10.9. Problems -- 11. Generalized Coordinates -- 11.1. Introductory Remarks -- 11.2. The Theory of Generalized Coordinates -- 11.3. The Nature of Generalized Coordinates -- 11.4. The ? Operator for Generalized Coordinates -- 11.5. Exceptional Cases -- 11.6. Problems -- 12. The Fundamental Equation in Generalized Coordinates -- 12.1. The Kinetic Energy -- 12.2. Two Equalities -- 12.3. The Fundamental Equation -- 12.4. Generalized Potential Forces -- 12.5. Velocity-Dependent Potentials -- 12.6. Problems -- 13. Lagrangeโs Equations -- 13.1. The Dynamical Problem -- 13.2. The Multiplier Rule -- 13.3. Derivation from the Fundamental Equation -- 13.4. Derivation from the Central Principle -- 13.5. Derivation from Hamiltonโs Principle -- 13.6. Dynamic Coupling and Decoupling -- 13.7. Special Forms of Lagrangeโs Equations -- 13.8. The Principle of LeastAction Reconsidered -- 13.9. Problems -- 14. Embedding Constraints -- 14.1. Introductory Remarks -- 14.2. A Fallacy -- 14.3. Embedding of Nonholonomic Constraints. -- 14.4. Problems -- 15. Formulating Problems by Lagrangeโs Equations -- 15.1. General Remarks -- 15.2. The Unconstrained Particle -- 15.3. The Holonomically Constrained Particle -- 15.4. The Nonholonomically Constrained Particle -- 15.5. Systems of Particles and Rigid Bodies -- 15.6. Problems -- 16. The Integration -- 16.1. The Meaning of an Integral -- 16.2. Jacobiโs Integral -- 16.3. TheRouthianFunctionandtheMomentumIntegrals -- 16.4. Partial and Complete Separation of Variables -- 16.5. Solution in Quadratures -- 16.6. Qualitative Integration -- 16.7. Problems -- 17. Stability -- 17.1. Introductory Remarks -- 17.2. Definition of Stability -- 17.3. The Variational Equations -- 17.4. Some Remarks on Indirect Methods -- 17.5. Some Remarks on Liapunovโs Direct Method -- 17.6. Problems -- 18. Applications -- 18.1. Introductory Remarks -- 18.2. The Single Particle -- 18.3. Systems of Particles -- 18.4. Nonholonomic Systems -- 18.5. Problems -- 19. About Celestial Problems -- 19.1. Historical Notes -- 19.2. The Central Force Problem -- 19.3. The Central Force Problem ContinuedโThe Apsides -- 19.4. The Central Force Problem ContinuedโOn Bertrandโs Theorem -- 19.5. The n-Body Problem -- 19.6. The Two-Body Problem -- 19.7. Some Information about the Three-Body Problem -- 19.8. Problems -- 20. Topics in Gyrodynamics -- 20.1. Introduction -- 20.2. The Heavy Symmetrical Top -- 20.3. The Gyroscope -- 20.4. The Gyrocompass -- 20.5. Problems -- 21. Impulsive Motion -- 21.1. General Remarks -- 21.2. The Fundamental Equation -- 21.3. Impulsive Constraints -- 21.4. The Fundamental Equation with Impulsive Constraints -- 21.5. Impulsive Motion Theorems -- 21.6. Lagrangeโs Equations for Impulsive Motion -- 21.7. Problems