Index
A
Absolute convergence, 402
Absolute extremum, 96
Absolute extremum function, 96
Absolutely convergent, 402
Absolute maximum, 96
Absolute maximum function, 96
Absolute minimum, 96
Absolute minimum function, 96
Abstract function, 404
Abstract space, 389
Accumulation point, 391
Action, 550
Active force, 515
Actual displacement, 516
Actual motion, 516
Actual path, 516
Actual work, 518
Additive operator, 405
Additivity, 394
Adjoint Hamiltonian operator train, 707, 730
Adjoint mirror image Hamiltonian operator
train, 730
Adjoint number, 69
Adjoint operator, 408, 409
Adjoint space, 408
Adjoint tensor, 613
Admissible class function, 96
Admissible condition, 91
Admissible curve, 110
Admissible curve class, 95
Admissible curve family, 95
Admissible displacement, 530
Admissible function, 91, 95
Admissible strain, 530
Admissible stress, 530
Admissible surface class, 95
Admissible surface family, 95
Algebraic number field, 388
α-th Lipschitz condition, 438
Alternating tensor, 54
Angle of transversality, 246
Anisochronal variation, 99
Anisochronous variation, 99
Anti-symmetric tensor, 61
Applied force, 515
Argument, 91
Argument function, 91
Ascending order operator, 695
Assigned index, 53
Associated Laguerre equation, 423
Associated Legendre equation, 423
Auxiliary functional, 320
B
Banach space, 394
Base, 51
Base function, 464
Base vector, 51
Basic set, 386, 389
Basis, 51
Basis function, 464
Bessel equation, 423
Bessel inequality, 403
Biharmonic equation, 165
Biharmonic function, 42, 165
Biharmonic operator, 42
Bijection, 387
Bijective mapping, 387
Bilateral constraint, 515
Bilinear functional, 104
Bolza(’s) problem, 345
Border, 391
© Beijing Institute of Technology Press and Springer Nature Singapore Pte Ltd. 2021
D. Lao and S. Zhao, Fundamental Theories and Their Applications of the Calculus
of Variations, https://doi.org/10.1007/978-981-15-6070-5
979
A
Absolute convergence, 402
Absolute extremum, 96
Absolute extremum function, 96
Absolutely convergent, 402
Absolute maximum, 96
Absolute maximum function, 96
Absolute minimum, 96
Absolute minimum function, 96
Abstract function, 404
Abstract space, 389
Accumulation point, 391
Action, 550
Active force, 515
Actual displacement, 516
Actual motion, 516
Actual path, 516
Actual work, 518
Additive operator, 405
Additivity, 394
Adjoint Hamiltonian operator train, 707, 730
Adjoint mirror image Hamiltonian operator
train, 730
Adjoint number, 69
Adjoint operator, 408, 409
Adjoint space, 408
Adjoint tensor, 613
Admissible class function, 96
Admissible condition, 91
Admissible curve, 110
Admissible curve class, 95
Admissible curve family, 95
Admissible displacement, 530
Admissible function, 91, 95
Admissible strain, 530
Admissible stress, 530
Admissible surface class, 95
Admissible surface family, 95
Algebraic number field, 388
α-th Lipschitz condition, 438
Alternating tensor, 54
Angle of transversality, 246
Anisochronal variation, 99
Anisochronous variation, 99
Anti-symmetric tensor, 61
Applied force, 515
Argument, 91
Argument function, 91
Ascending order operator, 695
Assigned index, 53
Associated Laguerre equation, 423
Associated Legendre equation, 423
Auxiliary functional, 320
B
Banach space, 394
Base, 51
Base function, 464
Base vector, 51
Basic set, 386, 389
Basis, 51
Basis function, 464
Bessel equation, 423
Bessel inequality, 403
Biharmonic equation, 165
Biharmonic function, 42, 165
Biharmonic operator, 42
Bijection, 387
Bijective mapping, 387
Bilateral constraint, 515
Bilinear functional, 104
Bolza(’s) problem, 345
Border, 391
© Beijing Institute of Technology Press and Springer Nature Singapore Pte Ltd. 2021
D. Lao and S. Zhao, Fundamental Theories and Their Applications of the Calculus
of Variations, https://doi.org/10.1007/978-981-15-6070-5
979