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| Desloge E.A. — Classical Mechanics. Volume 1 |
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| Ïðåäìåòíûé óêàçàòåëü |
Force, gravitational 60 — 61
Force, instantaneous action at distance 61
Force, internal 65 215
Force, interparticle 216
Force, inverse square 178 — 184 601
Force, irrotational 113 243
Force, line of action 256
Force, Lorentz transformation 885 — 886
Force, net 219
Force, net external 67 216
Force, Newtonian 59 — 62
Force, of constraint see Constraint forces
Force, ordinary 518 — 519
Force, parallel 261
Force, passive 528
Force, physical 517
Force, point of application 77 255
Force, reduction of systems 258
Force, relativistic 885 — 886
Force, representation 78
Force, specification 77
Foucault pendulum 138 — 139
Four-force 898
Four-momentum 897
Four-velocity 896
Frames of reference, inertial 11 — 12 857
Frames of reference, relative motion 32
Frames of reference, transformation between 13 — 21 859-
Frequencies of system 810
Frequency, resonance 164
Friction 75 — 76 80
Function 968
Functional dependence 460 — 463
Functional, definition 968
Functional, in Hamilton’s modified principle 843
Functional, in Hamilton’s principle 839
Functional, stationary values 972 — 975
Galilean transformation 13 20
Galileo 12
Gauss’s theorem 412
General tensors 921 — 927
Generalized components of force, and Euler angles 654 — 655
Generalized components of force, as covariant components 572
Generalized components of force, Cartesian components 355
Generalized components of force, definition 354 515
Generalized components of force, derived from potential function 356
Generalized components of force, determination 355 357 516
Generalized components of force, for holonomic constraint 356
Generalized components of force, for holonomic system 539 — 541
Generalized components of force, for quasi-coordinates 712
Generalized components of force, transformation 516 — 517
Generalized components of impulse 588
Generalized coordinates 352 — 353 514 539
Generalized force see Generalized components of force
Generalized force functions 558 — 562
Generalized momentum, conservation 577 578 585
Generalized momentum, definition 387 577 737
Generalized potential 558 — 560
Generalized velocities 352 514 539
Generating functions 789 — 795
Geometry of space 8
Gibbs — Appell equations of motion 720 — 725 727
Gibbs — Appell function 721 725 727
Gradient 408 — 409 414 424
Gram — Schmidt orthogonalization 674 915
Gravitational constant 73
Gravitational force, due to arbitrary mass distribution 74
Gravitational force, due to spherically symmetric mass distribution 74
Gravitational force, effective 139
Gravitational force, of homogeneous disk 78
Gravitational force, reduction to single force 262
Gravity, acceleration due to 73
Gravity, law 73
Green’s theorems 410 — 412
Group theory 945 — 950
Group, abelian 948
Group, automorphic 948
Group, complete Lorentz 893
Group, conjugate elements in 950
Group, cyclic 948
Group, definition 945
Group, homomorphic 948
Group, inhomogeneous Lorentz 893
Group, isomorphic 948
Group, Lorentz 893
Group, matrix representation 955
Group, of symmetry operations 685
Group, operator representation 955
Group, order 945
Group, periodic 948
Group, Poincare 893
Group, properties 945 — 946
Group, special Lorentz 894
Hamilton — Jacobi equation, for particle in central force field 803
Hamilton — Jacobi equation, for simple harmonic oscillator 802 — 803
Hamilton — Jacobi equation, generalization 801 — 802
Hamilton — Jacobi equation, solution by separation of variables 800 — 801
Hamilton — Jacobi equation, time-dependent 797 — 799
Hamilton — Jacobi equation, time-independent 799 — 800
Hamiltonian function 738
Hamiltonian, and total energy 388 738
Hamiltonian, canonical transformation 774 782
Hamiltonian, conservation 390 — 391 576 585 739
Hamiltonian, definition 387 — 388 737
Hamiltonian, importance 390
Hamiltonian, of particle in electromagnetic field 740
Hamiltonian, relativistic 903
Hamiltonian, transformation 774 791
Hamilton’s canonical equations of motion 773 — 782
Hamilton’s characteristic function, and Hamilton’s principle 840 — 841
Hamilton’s characteristic function, definition 800
Hamilton’s characteristic function, for particle in electromagnetic field 740 — 741
Hamilton’s characteristic function, for simple harmonic oscillator 802
Hamilton’s characteristic function, in condensed notation 769
Hamilton’s characteristic function, of second kind 744 — 745
Hamilton’s characteristic function, relativistic 903
Hamilton’s equations of motion 387 — 391 737
Hamilton’s modified principle 843 — 852
Hamilton’s principal function, definition 798
Hamilton’s principal function, for particle in central force field 804
Hamilton’s principal function, for simple harmonic oscillator 802
Hamilton’s principle 838 — 841
Hamilton’s principle, relation to modified Hamilton’s principle 845
Harmonic motion 158 — 168 373 665
Harmonic oscillator, simple, amplitude 161
Harmonic oscillator, simple, angular frequency 161
Harmonic oscillator, simple, critically damped 162
Harmonic oscillator, simple, damped 160 — 162
Harmonic oscillator, simple, decay modulus 161
Harmonic oscillator, simple, driven 162
Harmonic oscillator, simple, effect of constant force 166
Harmonic oscillator, simple, frequency 161
Harmonic oscillator, simple, overdamped 161
Harmonic oscillator, simple, period 161
Harmonic oscillator, simple, relaxation time 161
Harmonic oscillator, simple, solution by canonical transformation 782 — 783
Harmonic oscillator, simple, solution by Hamilton — Jacobi technique 802 — 803
Harmonic oscillator, simple, underdamped 160
Harmonic system 373 665 684
Holonomic constraints 349 — 351 356 531
Holonomic systems 351 — 352 538
Homomorphic group 948
Hooke’s law 74
Hooke’s law potential, motion in 602
Huygens, Christian 12
Ideal constraint force 529 — 531
Identity element in group 945 946 950
Ignorable coordinate 577
Impact parameter 188 615
Impulse, angular 127 129
| Impulse, definition and properties 126 — 132
Impulse, generalized components 588
Impulse, instantaneous 127 128 130 338 588
Impulse, on harmonic oscillator 167
Impulsive equations of motion, for particle 126 — 132
Impulsive equations of motion, for rigid body 338 — 341
Impulsive equations of motion, Lagrange’s 588 — 590
Indices, raising and lowering 925 — 926
Inertia ellipsoid 291
Inertia tensor 286 — 298 647
Inertia, law of 12
Inertia, moment of see Moment of inertia
Inertial forces 137
Inertial frames 11 — 12 857
Initial conditions 435
Integral, differentiation 441
Integral, line 409
Integral, surface 409 — 410
Integral, volume 409 — 410
Interaction between particles 59 875
Internal forces 215
Interparticle forces 216
Invariable line 330
Invariable plane 330
Invariant subgroup 949
Invariant subspace 686 953 963
Inverse of element in group 945 946 950
Inverse square force field, motion in 178 — 184 601
Inverse transformations 909 — 911
Irreducible representations, and natural modes 689 — 692
Irreducible representations, definition and properties 959 — 963
Irreducible subspace, of configuration space 686 — 687
Irreducible subspace, properties 963
Irrotational force field 113
Isomorphic groups 947 — 948
Jacobian elliptic functions 330 467
Jacobian, and inverse transformation 909
Jacobian, definition 401
Jacobian, for canonical transformation 760 771 794
Jacobian, in change of integration variables 912 — 913
Jacobian, of transformation from lab to center of mass 630
Jacobian, properties 401
Jacobi’s identity 824
Kinematics, Newtonian 7 — 46
Kinematics, of rigid body 303 — 319 647
Kinematics, relativistic 857 — 871
Kinetic energy, and work 107 — 108 234
Kinetic energy, average, for driven oscillator 163
Kinetic energy, change in collision 623
Kinetic energy, definition 107 234
Kinetic energy, generalized coordinates 524 — 525
Kinetic energy, of dynamical system 234
Kinetic energy, of particle 107 234
Kinetic energy, of rigid body 271 — 272 312 650
Kinetic energy, of two-particle system 198
Kinetic energy, relative 623
Kronecker delta 34 405
Laboratory coordinates 205 624 632
Lagrange bracket 757 770 825
Lagrange multipliers 53 464 533 880 970
Lagrange points 639 — 643
Lagrange’s equations of motion, and Hamilton’s principle 840
Lagrange’s equations of motion, and tensor analysis 570 — 572
Lagrange’s equations of motion, for anholonomic systems 554 — 556
Lagrange’s equations of motion, for elementary systems 521 — 526
Lagrange’s equations of motion, for holonomic systems 361 — 365 538
Lagrange’s equations of motion, for impulsive forces 588 — 590
Lagrange’s equations of motion, for Lagrangran systems 564 — 566
Lagrange’s equations of motion, for quasi-coordinates 715 — 719
Lagrange’s equations of motion, for rigid body 653 — 655
Lagrange’s equations of motion, harmonic 373 665 682
Lagrange’s equations of motion, relativistic form 901
Lagrangian system 564
Lagrangian, approximately 375 — 376 668
Lagrangian, definition 363 564
Lagrangian, indeterminate nature 566
Lagrangian, invariance 578 — 581 585
Lagrangian, normal coordinates 674
Lagrangian, relativistic 901
Laplacian 425
Latitude, definition 140
Left-handed systems 406
Legendre transformation, definition and properties 918 — 920
Legendre transformation, of kinetic energy 744
Legendre transformation, of Lagrangian 737 746
Length, contraction 868
Length, definition 7
Length, measurement 7
Levi — Civita symbol 35 321 407 423 562
Line integral, definition and properties 409 — 414
Line integral, independence of path 443 — 446
Line of nodes 303
Linear differential equations 436 — 440
Linear equations, system 458 — 459
Linear momentum, and force 59 218 885
Linear momentum, at arbitrary point 101 218
Linear momentum, at center of mass 219
Linear momentum, conservation 57 122 248 578 883
Linear momentum, definition, for particle 57 101
Linear momentum, definition, for system of particles 218
Linear momentum, definition, relativistic 883 — 884
Linear momentum, effect of impulse 126 — 130 338
Linear momentum, Lorentz transformation 884
Linear momentum, time rate of change 59 220 885
Linear operator representation, of group 955 — 966
Linear operator representation, of symmetry group 686
Linear operator, matrix representation 954
Linear operator, on vector space 953
Linear transformations 472 676
Logarithmic decrement 161
Lorentz force 561 741
Lorentz group 893 — 894
Lorentz transformation, consequences 867 — 869
Lorentz transformation, four-dimensional formulation 893 — 895
Lorentz transformation, in vector form 18 — 20 860
Lorentz transformation, of accelerations 863 — 864
Lorentz transformation, of force 885 — 886
Lorentz transformation, of linear momentum 884
Lorentz transformation, of velocities 861 — 863
Lorentz transformation, statement and derivation 13 — 21 859
Mass 56 — 57 883
Matrix addition 447 451
Matrix equality 447
Matrix multiplication 448 451
Matrix representation, of group 955
Matrix representation, of linear operator 954
Matrix representation, of vector 953
Matrix transformation, congruent 929
Matrix transformation, definition 928
Matrix transformation, equivalence 928
Matrix transformation, orthogonal 930
Matrix transformation, similarity 929
Matrix, adjoint 455
Matrix, adjugate 455
Matrix, antisymmetric 450
Matrix, augmented 459
Matrix, coefficient 459
Matrix, column 449
Matrix, complex conjugate 449
Matrix, congruent 929
Matrix, definition 447
Matrix, diagonal 450 932
Matrix, diagonalization 935 — 936
Matrix, eigenvalues 931 — 934
Matrix, equivalent 928
Matrix, inverse 455 — 456
Matrix, non-negative 450
Matrix, non-singular 455
Matrix, order 447
Matrix, orthogonal 456 930
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