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| Desloge E.A. — Classical Mechanics. Volume 1 |
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| Ïðåäìåòíûé óêàçàòåëü |
Abelian group 950
Absolute derivative 926 — 927
Acceleration, in cylindrical coordinates 45
Acceleration, in moving frame 38
Acceleration, in spherical coordinates 45
Acceleration, of gravity 73 74
Acceleration, relative 27
Action and angle variables 807 — 814
Action and reaction, law of 60 66 216
Action at distance 56
Amonton’s law of friction 75
Angular frequency 160
Angular frequency, of driven oscillator 163
Angular impulse 127 129
Angular momentum, and arbitrary point 102 226
Angular momentum, and center of mass 227
Angular momentum, and torque 103 229
Angular momentum, axial component 271 — 272
Angular momentum, change due to impulse 127 129 130 338
Angular momentum, conservation 123 174 248 580 585 586 598
Angular momentum, definition 102 226
Angular momentum, of incident particle 191
Angular momentum, of rigid body 271 272 312
Angular momentum, Poisson bracket of components 830
Angular momentum, time rate of change 103 229
Angular Motion 176 — 177 600
Angular velocity 33 — 36
Angular velocity, definition and properties 33 — 38
Angular velocity, Euler angles 310 650
Anholonomic constraint 532
Anholonomic system, and Gibbs — Appell equations 722 — 725
Anholonomic system, definition 554
Aphelion 184
Apocentron 183
Appell’s equations of motion 722
Appell’s function 721
Apse 177 600
Apsidal angle 177 600
Apsidal distance 177 600
Apsidal radius 600
Apsis 177 600
Associative law 945
Automorphic group 948
Axial direction 269
Axis of rotation, instantaneous 36
Basis vectors 683
Bertrand’s theorem 606 — 613
Bilinear form 928
Bound orbit 606 607
boundary conditions 435
Brachistochrone problem 979
Calculus of variations 968 — 980
Canonical transformation, and modified Hamilton’s principle 846 — 852
Canonical transformation, definition 755 — 756 762
Canonical transformation, inverse 761
Canonical transformation, Jacobian for 760 771 794
Canonical transformation, Lagrange bracket test 757
Canonical transformation, Poisson bracket test 826
Canonical transformation, product of two 761 — 762
Canonical transformation, properties 759 — 762
Canonical variables 773 — 774
Carrier space 955
Cartesian configuration space 240 — 241 349 514
Cartesian tensors 417 — 425
Cartesian vector quantity 421
Cartesian vectors 420 — 421 424
Center of mass, acceleration 67 217
Center of mass, coordinates 205 624 632
Center of mass, definition 66
Center of mass, determination 67
Center of mass, motion 67 — 68 197 216 220 254 274 320 655
Center of mass, of rigid body 269
Center of mass, of two particles 196 622
Center of mass, position 217
Center of mass, properties 65 — 68
Center of mass, table of values 479 — 482
Center of mass, uniqueness 66
Center of mass, velocity 217 622
Central force 172 — 174
Central force motion, angular motion 176 — 177 600
Central force motion, circular 606 — 607
Central force motion, for two-particle system 198
Central force motion, fundamental equations 175 598
Central force motion, Hamilton — Jacobi treatment 803 — 804
Central force motion, Lagrangian treatment 597 — 602
Central force motion, Newtonian treatment 172 — 184
Central force motion, orbit in 175 599
Central force motion, radial motion in 176 599
Central force motion, stability of circular orbit in 184
Central force motion, symmetry of orbit 600
Centrifugal force 138
Character table 689 — 690
Character, of matrix group element 961
Character, of operator 961
Character, of representations 961 — 963
Characteristic equation 931
Christoffel symbols 926
Circular motion in central force field 606 — 607
Class of element in group 950 960 962
clocks 9
Closed orbit 607
Closed systems 215
Closure law 945
Coefficient of kinetic friction 76
Coefficient of restitution 131 339
Coefficient of static friction 75
Collision, change in energy in 204 623
Collision, definition 49 — 50 203 622 875
Collision, description 203 622
Collision, elastic 131 204 339 623
Collision, inelastic 131 339
Collision, of particle with surface 131 — 132
Collision, possible 50 876
Collision, properties 50 876
Collision, quantities conserved in 52 — 56 876-
Collision, rigid body 339
Collision, two-particle 203 — 209 622
Colonization of space 643
Column matrix 449
Column matrix representation of vector 683 953
complex numbers 437
Complex of group 949
Compression period 131 339
Configuration of harmonic system 684
Configuration of system 241 513
Configuration space, basis vectors in 683
Configuration space, Cartesian 240 — 241 349 514
Configuration space, decomposition, by group theory 688
Configuration space, definition 241 514
Configuration space, for holonomic system 539 682
Configuration space, modal directions in 683
Configuration space, vector in 682 — 683
Conjugate elements in group 950
Conservation see also Constants of motion
Conservation, of angular momentum 123 174 248 580 585 586 598
Conservation, of energy 123 174 249 598 888
Conservation, of four-momentum 897
Conservation, of linear momentum 57 122 248 578 883
Conservation, of mass 57
Conservative force field 114 — 115 244
Conserved quantities 50 — 58 876 Constants
Constants see Constants of motion
Constants of motion see also Conservation Conserved
Constants of motion, and symmetry 578 — 584
Constants of motion, definition 120 247 575
Constants of motion, generalized coordinate as 740
Constants of motion, generalized momentum as 577 — 578 585 740
Constants of motion, Hamiltonian as 576 — 577 585 739 829
Constants of motion, importance 122 247
Constants of motion, in central force motion 174
| Constants of motion, in Hamiltonian formulation 390 739-
Constants of motion, in Lagrangian formulation 364 — 365 575
Constants of motion, in Poisson formulation 829
Constants of motion, in restricted three-body problem 638
Constants of motion, number of independent 120 — 121 247 575
Constants, in solution of differential equation 433 — 434
Constants, table 477
Constraint 349 528
Constraint forces, anholonomic: definition 532
Constraint forces, definition 349 528
Constraint forces, determination 549 — 550 555
Constraint forces, generalized components 532 — 534 541
Constraint forces, geometric 529
Constraint forces, holonomic, definition 349 — 351 531
Constraint forces, ideal 529 — 531
Constraint forces, kinematic 529
Contact, perfectly rough 76
Contact, perfectly smooth 76
Contraction of tensor 422
Contravariant vector 923
Conversion factors, table 478 — 479
Coordinate transformations 470 — 474
Coordinates, center of mass 205 624 632
Coordinates, generalized 352 — 353 514 539
Coordinates, laboratory 205 624 632
Coordinates, orthogonal curvilinear 43 — 46 427
Coordinates, relative 205 624 632
Coriolis force 138
Coset 949
Couple 256 — 257
Coupled oscillators 676 (see also Vibrating systems)
Covariant derivative 927
Covariant vector 923
Cross product 425
Cross section, differential scattering see Differential scattering cross section
Cross section, hard sphere 192 — 193 619
Cross section, inverse square 193 619
Cross section, total scattering 187 — 188 614 628
Curl 408 — 409 414 416 425
Curvilinear coordinates, orthogonal, equations of motion in 144 — 145
Curvilinear coordinates, orthogonal, properties 43 — 46 427
Cyclic coordinate 577 747
Cyclic group 948 950
Cyclic system 808
Cylindrical coordinates, definition and properties 44 — 45 429
Cylindrical coordinates, d’Alambert’s principle 56
Cylindrical coordinates, equations of motion in 144
Cylindrical coordinates, relation to rotating frame 45
Damped harmonic oscillator 160 — 162
Decay modulus 161
decrement 161
Degeneracy 686 — 687
Degrees of freedom 352 534
Del operator 409
Derivative, absolute 926 — 927
Descartes, Rene 12
Determinant 452 — 454 930
Diagonalization of matrices 935 — 936
Differential equations, linear 436 — 440
Differential equations, ordinary 432 — 435
Differential scattering cross section, center of mass 207 — 208 627 631
Differential scattering cross section, definition 188 — 189 615
Differential scattering cross section, determination 190 — 192 617
Differential scattering cross section, hard sphere 192 — 193 619
Differential scattering cross section, inverse square 193 619
Differential scattering cross section, transformation between lab and center of mass 208 — 209 629
Differential, exact 442 — 446
Differentiation, covariant 927
Differentiation, of integral 441
Differentiation, of tensor 424
Differentiation, partial 398 — 400
Dimension, irreducible 960
Dimension, of representation 955
Disk, rolling 534 — 536 556
Displacement, virtual 349 354 515 540 712
Dissipation function 560 — 561
Distance, shortest 978
Divergence 408 — 409 414 416 424
Dot product 403 424 425
Driven harmonic oscillator 162 — 168
Dynamical state 120
Dynamical system 65 215
Dynamics problems, method of solution 88
Dynamics, aim of 122
Effective potential 176 179 181 326 599
Eigencolumn 931
Eigenvalues of matrix 931 — 934
Einstein, Albert 12
Elastic collision 339
Electromagnetic field, generalized potential 561
Elementary system 521
Ellipsoid, of inertia 291
Ellipsoid, Poinsot 330
Elliptic functions 330 467
Energey, and momentum 888 — 889
Energy, and work 107 — 108 234 888
Energy, conservation 123 174 249 598 888
Energy, dissipation 164
Energy, kinetic see Kinetic energy
Energy, of acceleration 721
Energy, potential 888; see Potential energy relativistic
Equations of motion, Equations of motion, Gibbs — Appell 720 — 725 727
Equations of motion, Euler’s 322 656 719 730
Equations of motion, for two-particle system 197
Equations of motion, Hamiltonian type 744 — 747
Equations of motion, Hamilton’s see Hamilton’s equations of motion
Equations of motion, in configuration space 241
Equations of motion, Lagrange’s equations of motion, Newton’s see Newton’s equation
Equations of motion, of motion in non-inertial frames 136
Equations of motion, of rigid body 274 321
Equations of motion, Poisson’s 828 — 830
Equations of motion, relativistic 885 901 903
Equations of motion, Routh’s 746 — 749
Equilibrium points 638
Equimomental systems 323
Equivalence of matrices 928
Equivalent systems of forces 255 258
Escape speed 182 — 183
Euclidean set of coordinate systems 417
Euclidean transformation 473
Euler angles 303 — 307 649
Euler equation 972 — 974
Euler’s equations of motion 322 656 719 730
Euler’s theorem 914
Exact differentials 442 — 446
Extended point transformation 750 — 751 759
External forces 78 215
f function 763
Fictitious forces 137 — 138
Field 113 243 408 409 424
Fixed plane, definition 269
Force, action at distance 61 78
Force, active 528
Force, and linear momentum 218 — 220
Force, central 172 — 174
Force, classification 61
Force, components, generalized see Generalized components of force
Force, conservative 114 244
Force, contact 61 78
Force, coplanar 260
Force, definition 59 65 885
Force, derivable from generalized potential 559
Force, determination 77
Force, electromagnetic 61
Force, equivalent 77 255
Force, external 65 215 219
Force, fictitious 137 — 138
Force, field 113 243
Force, generalized components see Generalized components of force
Force, given 528
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