Biharmonic equation 82
Brachistochrone problem 57
Characteristic functions 83
Characteristic numbers 24 50 78 83
Conservative mechanical system 12
Constrained problem 26
Essentially positive E-functions 43
Euler — Lagrange equation 10 65 73 82 83
Extended phase matrix 29
Extended phase space 29
Extremal curve 10
Extremal field 35
Fermat’s principle of least time 56
Field function 35
Field matrix 35
Flux of a vector 73
Global uniqueness theorem 43
Hamilton-Jacobi equation 39
Hamiltonian canonical equations 30
Hamiltonian function 29
Hilbert invariant integral 38 66
Ignoration of coordinates 55
Index of refraction 56
Isotropic medium 56
Lagrangian function 2 71
Lagrangian integrand 4
Lagrangian momentum matrix 5
Lagrangian parameter 3
Legendre condition 19
Local uniqueness theorem 43
| Maximal curve 15
Minimal curve 14
Multiple integral problems 70
Normal derivative 82
Numerical space 2
Parametric Hamiltonian function 53
Parametric integrand 4
Parametric matrix 13
Parametric momentum matrix 5
Phase matrix 29
Piecewise-smooth curves 3
Positively definite matrix 24
Positively homogeneous function 4
Positively regular problems 45
Positively semidefinite matrix 25
Principle of Maupertais 56
Rayleigh quotients 51 67 78
Rayleigh — Ritz method 51
Singular point 27
Snell’s law of refraction 57
Spherically stratified medium 58
State space 7 71
Stratified medium 56
Strong Legendre condition 24
The Courant maximum-minimum principle 90
Transversal intersection 38
Transversality conditions 34
Undetermined multiplier 27
Variation 9
Weak Legendre condition 24
Weierstrass E-function 43
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