Classical DynamicsGraduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d'Alembert's principle and the idea of virtual work, Hamilton's equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends. 1977 edition. |
Contents
INTRODUCTORY CONCEPTS | 1 |
GENERALIZED COORDINATES | 4 |
CONSTRAINTS | 8 |
VIRTUAL WORK | 13 |
ENERGY AND MOMENTUM | 28 |
LAGRANGES EQUATIONS | 48 |
EXAMPLES | 56 |
INTEGRALS OF THE MOTION | 66 |
PHASE SPACE | 179 |
HAMILTONJACOBI THEORY | 187 |
HAMILTONS PRINCIPAL FUNCTION | 188 |
THE HAMILTONJACOBI EQUATION | 193 |
SEPARABILITY | 204 |
CANONICAL TRANSFORMATIONS | 214 |
SPECIAL TRANSFORMATIONS | 227 |
LAGRANGE AND POISSON BRACKETS | 241 |
SMALL OSCILLATIONS | 83 |
SPECIAL APPLICATIONS OF LAGRANGES EQUATIONS | 102 |
IMPULSIVE MOTION | 104 |
GYROSCOPIC SYSTEMS | 123 |
VELOCITYDEPENDENT POTENTIALS | 137 |
HAMILTONS EQUATIONS | 147 |
HAMILTONS EQUATIONS | 162 |
OTHER VARIATIONAL PRINCIPLES | 173 |
MORE GENERAL TRANSFORMATIONS | 249 |
MATRIX FORMULATIONS | 256 |
FURTHER TOPICS | 258 |
INTRODUCTION TO RELATIVITY | 272 |
RELATIVISTIC KINEMATICS | 277 |
RELATIVISTIC DYNAMICS | 298 |
ACCELERATED SYSTEMS | 315 |
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Common terms and phrases
applied forces axis canonical equations canonical transformation center of mass coefficients components configuration space constant constraint equations constraint forces corresponding degrees of freedom differential equations differential form dq's dynamics equal equations of motion example explicit function expression F₁ form of Eq form of Lagrange's Furthermore given in Eq gyroscopic Hamilton-Jacobi equation Hamilton's equations Hamilton's principle Hamiltonian Hamiltonian function Hence holonomic system ignorable coordinates impulse independent inertial frame initial conditions integral invariant Jacobi integral kinetic energy Lagrange bracket Lagrange's equations Lagrangian Lagrangian function let us consider linear m₁ matrix natural system nonholonomic nonzero obtain orthogonal P₁ phase space positive potential energy problem Q₁ relative relativistic result rotation Routhian sin² solution solve t₁ T₂ theory tion total energy trajectory transformation equations variables variation varied paths vector velocity virtual displacement zero дн др