|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Desloge E.A. — Classical Mechanics. Volume 1 |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Matrix, positive definite 450 932
Matrix, positive semidefinite 450 932
Matrix, properties 451
Matrix, rank 457 459
Matrix, regular 455
Matrix, row 449
Matrix, scalar 450
Matrix, similar 929 932
Matrix, singular 455
Matrix, skew-symmetric 450
Matrix, square 450
Matrix, submatrix 457
Matrix, symmetric 450 932
Matrix, trace 961
Matrix, transposition 448 451
Matrix, unit 450 — 451
Matrix, unitary 457
Matrix, zero 449 451
Mechanics, definition 1
Metric tensor 896 925
Modal direction 374 666 671 683
Modal frequency 374 666 683 688 692
Modal vector 374 666 673 683
Modified Hamilton’s principle 843 — 852
Modified velocity 865 876
Modulus of elasticity 75
Moment of inertia, definition and properties 269 — 271 286 647
Moment of inertia, principal 292 — 295 648
Moment of inertia, table of values 482 — 486
Moment of mass 66
Momentum, and energy, relativistic relation between 888 — 889
Momentum, angular see Angular momentum
Momentum, linear see Linear momentum
Motion, central force see Central force motion
Motion, constants of see Constants of motion
Motion, equations see Equations of motion
Motion, harmonic 158 — 168 373 665
Motion, impulsive 126 — 132 338 588
Motion, of center of mass 67 — 68 197 216 220 254 274 320 655
Motion, of particles 27 — 28
Motion, one-dimensional 151 — 156
Motion, relative: of frames of reference 32 — 39
Motion, uniplanar 269 — 275
Multiplication table for group 947 — 948
Multiplicity, of degeneracy 686 — 687
Multiplicity, of modal frequency 688 — 689
Multiply periodic function 810 967
Natural coordinates 376 — 378 670
Natural modes of motion, definition and properties 373 — 376 665
Natural modes of motion, determination, using group theory 682 — 695
Natural modes of motion, superposition 377 671
Newton, Isaac 12
Newton’s equation of motion, and d’Alembert’s principle 835
Newton’s equation of motion, and Lagrange’s equations 361 — 363 522
Newton’s equation of motion, and torque-angular momentum theorem 103
Newton’s equation of motion, and work-energy theorem 108
Newton’s equation of motion, application to elementary problems 88 — 89
Newton’s equation of motion, for system of particles 216 240 513
Newton’s equation of motion, impulsive form 126
Newton’s equation of motion, in configuration space 240 — 242 513
Newton’s equation of motion, in cylindrical coordinates 144
Newton’s equation of motion, in non-inertial frames 136 — 139
Newton’s equation of motion, in spherical coordinates 145
Newton’s equation of motion, in tensor form 570 — 571
Newton’s equation of motion, statement 59 — 60 102
Newton’s law for collisions 339
Newton’s law of gravity 73
Newton’s laws see also Newton’s equation of motion
Newton’s laws, first law 12
Newton’s laws, second law 59 — 60
Newton’s laws, third law 60 — 61
Nodes, line of 303
Noether’s theorem 581 — 586
Normal coordinates 378 673
Normal divisor 949
Nutation 326
Operator, linear see Linear operator
Operator, projection 690 — 691 964
Orbit, bound 606
Orbit, in central force motion 175 599
Orbit, in inverse square force field 180 182 601
Order, of cyclic group 948
Order, of element in group 947
Order, of group 945
Orthogonal curvilinear coordinates see Curvilinear coordinates
Orthogonal matrix 456
Orthogonal transformation 473
Orthogonality condition, for irreducible representations 961 — 962
Orthogonality condition, for modal vectors 67 3
Oscillations, small see Vibrating systems
oscillators see also Vibrating systems
Oscillators, coupled 676
Oscillators, harmonic see Harmonic oscillator
Parallel-axis theorem 270 290
Partial differentiation 398 — 400
Particles, collisions between 203 — 209 622
Particles, definition 1 — 2
Particles, equations of motion see Equations of motion
Particles, interaction 49
Particles, relative motion 27 — 28
Particles, statics 83 — 85
Particles, system of two 196 — 200
Pericentron 183
Perihelion 183
Period, fundamental 813 916
Period, in oscillatory one-dimensional motion 153 — 156
Period, of harmonic oscillator 159
Period, of inverse square orbit 183
Period, of multiply periodic function 813 916
Periodic group 948
Permutation symbol 35 321 407 423 562
Phase angle 163
Poincare group 893
Poinsot ellipsoid 330
Point transformation 750 — 751
Poisson brackets 759 823
Poisson’s equations of motion 828 — 830
Poisson’s hypothesis 339
Poisson’s theorem 829
POSITION 27 38 45 196
Postulates of mechanics, classical, I 11
Postulates of mechanics, classical, I I 12
Postulates of mechanics, classical, III 20
Postulates of mechanics, classical, IV 56
Postulates of mechanics, classical, V 216
Postulates of mechanics, relativistic, I 857
Postulates of mechanics, relativistic, II 857
Postulates of mechanics, relativistic, III 858
Postulates of mechanics, relativistic, IV 883
Potential energy, and work 115 244
Potential energy, average, for driven oscillator 163
Potential energy, definition and properties 113 — 115 243
Potential energy, determination from orbit 178
Potential energy, gravitational 117
Potential energy, of harmonic oscillator 158
Potential function 114 243 560
Potential, effective 176 179 181 326 599
Potential, generalized 558 — 560
Potential, power law 600 — 602
Potential, single-valued 114 244
Power law potential 600 — 602
Power of group element 946 — 947
Principal axis 292 — 298 648
Principal directions 292 — 298 648
Principal moments of inertia 292 — 295 648
Product, cross 403 406
Product, dot 424
Product, scalar 403 424
Product, vector 403 424
Products of inertia 287
| Projection operator 690 — 691 964
Proper subspace 952
Quadratic forms, by orthogonal transformation 941 — 943
Quadratic forms, definition 937
Quadratic forms, properties 937
Quadratic forms, reduction to sum of squares: by linear transformation 939 — 941
Quadratic forms, simultaneous 943 — 944
Quadratic forms, transformation 938 — 939
Quadratic forms, types 937
Quasi-coordinates, and Gibbs — Appell equations 720 — 725
Quasi-coordinates, definition and properties 711 — 714
Quasi-coordinates, Lagrange’s equation 715 — 717
Quotient law 925
Radial motion 176 599
Reduced mass 198
Reducible representation 959 — 960
Reduction of quadratic form 939 — 943
Reference frames 7 9 23 136
Regular transformation 471
Relative coordinates 205 624 632-
Relative motion 27 — 28 32 197
Relativistic mechanics, basic postulates 857 — 858 883
Relativistic mechanics, dynamics 875 — 889
Relativistic mechanics, four-dimensional formulation 893 — 898
Relativistic mechanics, Hamilton’s equations in 903 — 904
Relativistic mechanics, kinematics 857 — 871
Relativistic mechanics, Lagrange’s equations in 901 — 902
Relativity see also Relativistic mechanics
Relativity, general theory 1
Relativity, principle 11 — 12
Relativity, special theory 1
Relaxation time 161 166
Representation, of operator by matrix 954
Representation, of quantity by tensor 921
Representation, of vector by matrix 953
Representations of group, characters 961 — 963
Representations of group, dimensions 955
Representations of group, direct sum 957
Representations of group, equivalence 962
Representations of group, equivalent 956
Representations of group, generation 957
Representations of group, irreducible 956 959
Representations of group, matrix 955
Representations of group, natural 958
Representations of group, one-dimensional 957
Representations of group, operator 686 955
Representations of group, reducible 959 — 960
Representations of group, regular 958 — 960
Representations of group, unitary 957
Resonance 164 — 166
Restitution, coefficient 131 339
Restitution, period 131 339
Restricted three-body problem 634 — 643
Riemannian space 896 925
Right-handed systems 406
Rigid body, angular momentum 271 — 273 312
Rigid body, collisions 339 — 341
Rigid body, configuration 253 — 254 271 303
Rigid body, definition 253
Rigid body, kinetic energy 271 — 273 312 650
Rigid body, statics 264 — 266
Rigid-body motion, dynamics 320 — 323 653
Rigid-body motion, equations of motion, Gibbs — Appell 727 — 730
Rigid-body motion, equations of motion, Lagrangian 653 — 655
Rigid-body motion, equations of motion, Newtonian 254 261 274 320
Rigid-body motion, impulsive 338 — 341
Rigid-body motion, kinematics 303 — 315 647
Rigid-body motion, uniplanar 269 — 275
Rocket 220
Rotating frames 33 — 39 136
Rotation, as transformation 474
Rotation, instantaneous axis 36 — 37
Rotational motion 33
Routhian 746
Routh’s equations of motion 746 — 749
scalar 402 419 922
Scalar field 408
Scalar potential 470
Scalar product 403 424
Scattering angle 188 — 192 205 618 624
Scattering cross section see Cross section
Separable systems 807
Separation of variables 800 — 801
Simple closed orbit 607
simple harmonic motion 158 — 168
Simple harmonic oscillator see Harmonic oscillator
Sine function 397
Space, absolute 22
Space, configuration see Configuration space
Space, definition 7
Speed of particle, upper limit 16 20 858
Sphere, rolling 332 — 333 658 730
Spherical coordinates, definition and properties 45 — 46 430
Spherical coordinates, equations of motion 145 525
Spherical coordinates, relation to rotating frame 45 — 46
Spring constant 74
Spring linear 74
Statics, of particle 83 — 85
Statics, of rigid body 264
Stationary value, of function 464 — 466 969
Stationary value, of functional 972 — 978
Steady-state solution 163
Stokes’ Theorem 413
strings 76 — 77
Subgroups 949 — 950
Summation convention 425 768 922
Surface, perfectly rough 76
Surface, perfectly smooth 76
Symmetric top see Top symmetric
Symmetry group 685 — 686
Symmetry operations 684 — 686
Symmetry, and constants of motion 578 — 584
Symmetry, and natural modes of motion 682 — 707
Tables 477 — 486
Tensors, and Lagrange’s equations of motion 570 — 572
Tensors, cartesian 288 417
Tensors, general 921 — 927
Tensors, in relativistic mechanics 893 — 898
Tensors, inertia 286 — 298 647
Tensors, metric 896 925
Three-body problem, restricted 634 — 643
Thrust of rocket 220
Time dilation 867 — 868
Time rate of change in different frames 33 — 36
Time, absolute 22
Time, definition 8
Time, measurement 8 — 9
Top, asymmetric 327 — 332
Top, spin 325
Top, stability of motion 658 — 659
Top, symmetric, freely rotating 323 — 325
Top, symmetric, in gravitational field 325 — 327 657 748
Torque, and angular momentum 103 229
Torque, at arbitrary point 103 227
Torque, at center of mass 228
Torque, axial component 273 — 274
Torque, definition 102 — 103 227
Torque, produced by couple 256 — 257
Total cross section 187 — 188 614 628
Trace of matrix 930 933
Transformation coefficients 308 418
Transformation matrices 307 308
Transformations, canonical see Canonical transformation
Transformations, congruent 929
Transformations, coordinate 470 — 474
Transformations, equivalence 928
Transformations, Galilean 13 20
Transformations, inverse 909 — 911
Transformations, lab to center of mass 206 — 209 625
Transformations, Lorentz see Lorentz transformation
|
|
|
| Ðåêëàìà |
|
|
|
|
|
|
|
|
Î ïðîåêòå