Ardema M.D. — Analytical Dynamics: Theory and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Ardema M.D. — Analytical Dynamics: Theory and Applications

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Название: Analytical Dynamics: Theory and Applications

Автор: Ardema M.D.

Аннотация:

This book takes a classical approach to the development of the methods of analytical dynamics. After a review of Newtonian dynamics, the basic concepts of analytical dynamics - classification of constraints, classification of forces, virtual displacements, virtual work and variational principles - are introduced and developed. Next, Lagrange's equations are derived and their integration is discussed. The Hamiltonian portion of the book covers Hamilton's canonical equations, contact transformations, and Hamilton-Jacobi theory. Also included are chapters on stability of motion, impulsive forces, and the Gibbs-Appell equation.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 340

Добавлена в каталог: 11.01.2010

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Предметный указатель

Acceleration of a point      4
Acceleration, possible      77
Accessibility of configuration, space      59
action      95
Actual motion      53
Angular acceleration      9
Angular velocity      9 18
Apoapsis      185
Assumptions, basic      1
Autonomous systems      47
Basic kinematic equation      10
Basic problems in kinetics      3
Bertrand’s theorem      235
Calculus of variations      90
Canonical equations      263
Carnot’s theorem      240
Center of mass      17
Central force motion      272
Central principle      86
Characteristic equation      212
Choice of coordinates      131
Classification of constraints      154
Classification of forces      80
Configuration space      49
Conic sections      183
Conservative force      14 78 113 119
Constrained particle      136
Constraint forces      66 68
Constraints, acatastatic      57
Constraints, catastastic      57
Constraints, configuration      56
Constraints, equality      56
Constraints, holonomic      51 57
Constraints, nonholonomic      51 56 137
Constraints, rheonomic      51
Constraints, scleronomic      51
Contact transformations      283
Continuous group of transformations      281
Continuous point transformations      287
coordinates      102
Coordinates, cylindrical      8 133
Coordinates, generalized      102
Coordinates, rectangular      132
Coordinates, spherical      8 135
Degrees of freedom      19 53
Descriptive function      120 264 301
Differential      76
Dirichlet’s stability theorem      221
Displacements, actual      66
Displacements, infinitesimal      54
Displacements, possible      66 104
Displacements, virtual      66 104
Disspative forces      156
distribution      225
DuBois - Reymond lemma      91
Dynamic coupling      122
Dynamics      3
Dynamics, problem of the first kind      3 48 65
Dynamics, problem of the second kind      3 48
d’Alembert’s principle      67
Eccentric annomaly      186
Eccentricity      183
Eigenvalues      212
Embedding constraints      124
Energy theorem      235
Euclidean space      1
Euler - Lagrange equation      90
Euler angles      191
Euler’s theorem      11
Event space      49
Extremal      90
Formulating problems      131
Functions, Liapunov      220
Functions, positive definite, definite, semi-definite, negative definite      219
Fundamental equation      67 78 112 228 232 249 262
Fundamental lemma      90
Gauss’s principle of least constraint      233
General potential functions      121
Generalized force      112
Generalized goordinates      102
Generalized momentum      158
Generating function      283
Gibbs — Appell equations      250
Gibbs’ function      249
Gibbs’ theorem      250
Given forces      66 78
Gradient      13
Gravitation      14
Gravitational constant      14
Gyrocompass      201
Gyroscope      199
Hamilton      307
Hamilton — Jacobi equation      304
Hamilton — Jacobi theorem      305
Hamiltonian function      262
Hamilton’s characteristic function      309
Hamilton’s equations      263
Hamilton’s principal function      298
Hamilton’s principle      87 117 122 297
Hamilton’s principle, first form      87
Hamilton’s principle, second form      87
Hamilton’s principle, third form      88
Heavy symmetrical top      192 315
Hill equations      217
Homogeneous contact transformations      286
Ignorable coordinates      158 282

Impulsive constraints      228 229
Impulsive constraints, inert      232
Impulsive constraints, live      232
Impulsive force      225
Inertial reference frame      1
Infinitesmal contact transformations      330
Integrals of motion      150
Invariance of Lagrange’s equations      123
Inverse square forces      182
jacobi      308
Jacobi’s integral      153
Jacobi’s integral, explicit form      153
Jacobi’s theorem      291
Jacobi’s theorem of the last multiplier      277
Kelvin’s theorem      237
Kepler’s laws, first      183
Kepler’s laws, second      180
Kepler’s laws, third      184
Kinematics      3
kinetic energy      13 83 109
Kinetics      3
Koenig’s theorem      21
Koenig’s theorem, analogue of      253
Lagrange      118
Lagrange brackets      288
Lagrange multipliers      70
Lagrange’s equations      117
Last multiplier      276
Liapunov’s theorem      220 222
Liouville systems      162
Liouville’s theorem      288
Mean anomaly      186
Mechanical energy      16
Momentum integral      159
Multiplier rule      70 115 116
Natural systems      263
Newtonian problem      47 225
Newton’s laws of motion      1 2
Newton’s Second Law      47
Non-minimal coordinates      121
Nonconservative forces      78
Noncontemporaneous variations      95
Normal-tangential components      5
Nutation      192
One-to-one      103
Onto      103
Orbit equation      182
Orbits, hyperbolic, parabolic, elliptical, circular      183
Particle dynamics      4
Periapsis      185
Pfaffian form      57 68
Poisson brackets      271
Poisson’s theorem      272
Possible motion      53
potential energy      13 113
Potential energy function      78
Power      12
Precession      192
Precession of the equinoxes      199
Principle of least action      94
Principle of least action, Jacobi’s      96
Principle of least action, Lagrange’s      95
Qualitative integration      151
Quasi-coordinates      246
Radius of curvature      7
Rayleigh’s dissipation function      120
Rectangular components      4
Relative velocity      9
Relativity theory      28
Rigid body      18 53 67
Rigid body dynamics      17
Routh — Hurwitz criteria      212
Routhian function      159
Separability      314
Separation of variables      162
Solution of dynamical system      151
Solution, closed form      151
Solution, in quadratures      151
Speed      4
Spin      192
Stability      206
Stability, Hamiltonian systems      268
Stability, Liapunov      208
Stability, orbital      210
Stability, Poincare      209
State space      50
State variable form      206
State vector      206
State-time space      50
Statics      3
Strictly Newtonian problem      47
Superposition theorem      234
Taylor’s Theorem      238
Time equation      186
Transformation of coordinates      102
True anomaly      185
Unconstrained particle      132
Uncoupled systems      162
Variation of a function      76
Variation of constants      319
Variation of the elements      325
Velocities, possible      77
Velocity of a point      4
Virtual change of state      74
Virtual velocity      74
Virtual work      66 76
Work      12

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