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Umfang: 1 online resource (xvii, 456 pages) : , digital, PDF file(s).

Ausgabe: 4th ed.

ISBN: 1-316-04314-2 , 0-511-60879-9

Serie: Cambridge mathematical library

Inhalt: This classic book is a encylopaedic and comprehensive account of the classical theory of analytical dynamics. The treatment is rigorous yet readable, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration, and dissipative systems. Hamilton's principle is introduced and then applied to dynamical systems, including three-body systems and celestial mechanics. Very many examples and exercisies are supplied throughout.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Cover -- Half-title -- Title -- Copyright -- Contents -- Foreword by Sir William McCrea, FRS -- Preface to the fourth edition -- Kinematical Preliminaries -- SECTION 1. The displacements of rigid bodies -- SECTION 2. Euler's theorem on rotations about a point -- SECTION 3. The theorem of Rodrigues and Hamilton -- SECTION 4. The composition of equal and opposite rotations about parallel axes -- SECTION 5. Chasles' theorem on the most general displacement of a rigid body -- SECTION 6. Halphen's theorem on the composition of two general displacements -- SECTION 7. Analytic representation of a displacement -- SECTION 8. The composition of small rotations -- SECTION 9. Euler's parametric specification of rotations round a point -- SECTION 10. The Eulerian angles -- SECTION 11. Connexion of the Eulerian angles with the parameters ξ, η, ζ, χ -- SECTION 12. The connexion of rotations with homographien: the Cayley-Klein parameters -- SECTION 13. Vectors -- SECTION 14. Velocity and acceleration -- their vectorial character -- SECTION 15. Angular velocity -- its vectorial character -- SECTION 16. Determination of the components of angular velocity of a system in terms of the Eulerian angles, and of the symmetrical parameters -- SECTION 17. Time-flux of a vector whose components relative to moving axes are given -- SECTION 18. Special resolutions of the velocity and acceleration -- Miscellaneous Examples -- The Equations of Motion -- SECTION 19. The ideas of rest and motion -- SECTION 20. The laws which determine motion -- SECTION 21. Force -- SECTION 22. Work -- SECTION 23. Forces which do no work -- SECTION 24. The coordinates of a dynamical system -- SECTION 25. Holonomic and non-holonomic systems -- SECTION 26. Lagrange's form of the equations of motion of a holonomic system -- SECTION 27. Conservative forces -- the kinetic potential. , SECTION 28. The explicit form of Lagrange's equations -- SECTION 29. Motion of a system which is constrained to rotate uniformly round an axis -- SECTION 30. The Lagrangian equations for quasi-coordinates -- SECTION 31. Forces derivable from a potential-function which involves the velocities -- SECTION 32. Initial motions -- SECTION 33. Similarity in dynamical systems -- SECTION 34. Motion with reversed forces -- SECTION 35. Impulsive motion -- SECTION 36. The Lagrangian equations of impulsive motion -- Miscellaneous Examples -- Principles Available for the Integration -- SECTION 37. Problems which are soluble by quadratures -- SECTION 38. Systems with ignorable coordinates -- SECTION 39. Special cases of ignoration -- integrals of momentum and angular momentum -- SECTION 40. The general theorem of angular momentum -- SECTION 41. The energy equation -- SECTION 42. Reduction of a dynamical problem to a problem with fewer degrees of freedom, by means of the energy equation -- SECTION 43. Separation of the variables -- dynamical systems of Liouville's type -- Miscellaneous Examples -- The Soluble Problems of Particle Dynamics -- SECTION 44. The particle with one degree of freedom -- the pendulum -- SECTION 45. Motion in a moving tube -- SECTION 46. Motion of two interacting free particles -- SECTION 47. Central forces in general: Hamilton's theorem -- SECTION 48. The integrable cases of central forces -- problems soluble in terms of circular and elliptic functions -- SECTION 49. Motion under the Newtonian law -- SECTION 50. The mutual transformation of fields of central force and fields of parallel force -- SECTION 51. Bonnet's theorem -- SECTION 52. Determination of the most general field of force under which a given curve or family of curves can be described -- SECTION 53. The problem of two centres of gravitation -- SECTION 54. Motion on a surface. , SECTION 55. Motion on a surface of revolution -- cases soluble in terms of circular and elliptic functions -- SECTION 56. Joukovsky's theorem -- Miscellaneous Examples -- The Dynamical Specification of Bodies -- SECTION 57. Definitions -- SECTION 58. The moments of inertia of some simple bodies -- SECTION 59. Derivation of the moment of inertia about any axis when the moment of inertia about a parallel axis through the centre of gravity is known -- SECTION 60. Connexion between moments of inertia with respect to different sets of axes through the same origin -- SECTION 61. The principal axes of inertia -- Cauchy's momental ellipsoid -- SECTION 62. Calculation of the angular momentum of a moving rigid body -- SECTION 63. Calculation of the kinetic energy of a moving rigid body -- SECTION 64. Independence of the motion of the centre of gravity and the motion relative to it -- Miscellaneous Examples -- The Soluble Problems of Rigid Dynamics -- SECTION 65. The motion of systems with one degree of freedom -- motion round a fixed axis, etc -- SECTION 66. The motion of systems with two degrees of freedom -- SECTION 67. Initial motions -- SECTION 68. The motion of systems with three degrees of freedom -- SECTION 69. Motion of a body about a fixed point under no forces -- SECTION 70. Poinsot's kinematical representation of the motion -- the polhode and herpolhode -- SECTION 71. Motion of a top on a perfectly rough plane -- determination of the Eulerian angle θ -- SECTION 72. Determination of the remaining Eulerian angles, and of the Cayley-Klein parameters -- the spherical top -- SECTION 73. Motion of a top on a perfectly smooth plane -- SECTION 74. Kowalevski's top -- SECTION 75. Impulsive motion -- Miscellaneous Examples -- Theory of Vibrations -- SECTION 76. Vibrations about equilibrium -- SECTION 77. Normal coordinates. , SECTION 78. Sylvester's theorem on the reality of the roots of the determinantal equation -- SECTION 79. Solution of the differential equations -- the periods -- stability -- SECTION 80. Examples of vibrations about equilibrium -- SECTION 81. Effect of a new constraint on the periods of a vibrating system -- SECTION 82. The stationary character of normal vibrations -- SECTION 83. Vibrations about steady motion -- SECTION 84. The integration of the equations -- SECTION 85. Examples of vibrations about steady motion -- SECTION 86. Vibrations of systems involving moving constraints -- Miscellaneous Examples -- Non-Holonomic Systems. Dissipative Systems -- SECTION 87. Lagrange's equations with undetermined multipliers -- SECTION 88. Equations of motion referred to axes moving in any manner -- SECTION 89. Application to special non-holonomic problems -- SECTION 90. Vibrations of non-holonomic systems -- SECTION 91. Dissipative systems -- frietional forces -- SECTION 92. Resisting forces which depend on the velocity -- SECTION 93. Rayleigh's dissipation-function -- SECTION 94. Vibrations of dissipative systems -- SECTION 95. Impact -- SECTION 96. Loss of kinetic energy in impact -- SECTION 97. Examples of impact -- Miscellaneous Examples -- The Principles of Least Action and Least Curvature -- SECTION 98. The trajectories of a dynamical system -- SECTION 99. Hamilton's principle for conservative holonomic systems -- SECTION 100. The principle of Least Action for conservative holonomic systems -- SECTION 101. Extension of Hamilton's principle to non-conservative dynamical systems -- SECTION 102. Extension of Hamilton's principle and the principle of Least Action to non-holonomic systems -- SECTION 103. Are the stationary integrals actual minima? Kinetic foci -- SECTION 104. Representation of the motion of dynamical systems by means of geodesies. , SECTION 105. The least-curvature principle of Gauss and Hertz -- SECTION 106. Expression of the curvature of a path in terms of generalised coordinates -- SECTION 107. Appell's equations -- SECTION 108. Bertrand's theorem -- Miscellaneous Examples -- Hamiltonian Systems and Their Integral-Invariants -- SECTION 109. Hamilton's form of the equations of motion -- SECTION 110. Equations arising from the Calculus of Variations -- SECTION 111. Integral-invariants -- SECTION 112. The variational equations -- SECTION 113. Integral-invariants of order one -- SECTION 114. Relative integral-invariants -- SECTION 115. A relative integral-invariant which is possessed by all Hamiltonian systems -- SECTION 116. On systems which possess the relative integral-invariant ∫∑pδq -- SECTION 117. The expression of integral-invariants in terms of integrals -- SECTION 118. The theorem of Lie and Koenigs -- SECTION 119. The last multiplier -- SECTION 120. Derivation of an integral from two multipliers -- SECTION 121. Application of the last multiplier to Hamiltonian systems -- use of a single known integral -- SECTION 122. Integral-invariants whose order is equal to the order of the system -- SECTION 123. Reduction of differential equations to the Lagrangian form -- SECTION 124. Case in which the kinetic energy is quadratic in the velocities -- Miscellaneous Examples -- The Transformation - Theory of Dynamics -- SECTION 125. Hamilton's Characteristic Function and contact-transformations -- SECTION 126. Contact-transformations in space of any number of dimensions -- SECTION 127. The bilinear covariant of a general differential form -- SECTION 128. The conditions for a contact-transformation expressed by means of the bilinear covariant -- SECTION 129. The conditions for a contact-transformation in terms of Lagrange's bracket expressions. , SECTION 130. Poisson's bracket-expressions. , English

Weitere Ausg.: ISBN 0-521-35883-3

Sprache: Englisch