## Separation of variables in the special diagonal Hamilton-Jacobi equation: application to the dynamical problem of a particle constrained on a moving surface |

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### Contents

INTRODUCTION | 1 |

SEPARATION OF THE SPECIAL DIAGONAL HAMILTONJACOBI EQUATION | 14 |

SOLUTIONS OF THE DYNAMICAL PROBLEM OF A PARTICLE CONSTRAINED | 27 |

3 other sections not shown

### Common terms and phrases

11 Stackel analytical mechanics arbitrary constants arbitrary functions automatically satisfied canonical transformations coefficients complete integral conditions in equations Constrained Particle contravariant metric tensor coordinate surfaces cosh d2 cosh2 d2 sinh2 degrees of freedom denotes diagonal Hamilton-Jacobi equation dT dt dynamical problems Eisenhart ref equation 11 equation 46 equation 63 equations 137 equations 72 Euclidean three-dimensional space F. K. Chan form n S(q,t;a form of equation g33 is independent given by equations Hamilton Hamilton's equations Hamiltonian Heat equation Jacobi equation kinetic energy Lagrange's equations lemma matrix momenta monotonic function moving surface necessary and sufficient orthogonal partial differential equation particle constrained particle moving Particle on Moving potential energy radial motion results of theorem separation of variables set of coordinates set of equations sin2 solution special diagonal Hamilton-Jacobi Spherical Coordinates Stackel coordinate systems sufficient conditions T2Xl time-dependent TQ(t Unconstrained vector X^xW X2 Yl yields