## Foundations of theoretical mechanics |

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### Contents

Elemental Mathematics | 15 |

Variational Approach to SelfAdjointness | 54 |

The Fundamental Analytic Theorems | 110 |

Copyright | |

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### Common terms and phrases

acting forces adjoint system admissible analysis analytic representation aspect assumption calculus of differential calculus of variations canonical characterize Chart computation conditions of self-adjointness configuration space conservative systems considered constraints context contravariant conventional coordinates couplings degenerate derivatives differential forms direct analytic representation dissipative forces equations of motion equations of variations equivalent existence first-order Fundamental Analytic Theorem fundamental form geometrical given Hamilton's equations Hamilton's principle Hamiltonian holonomic identifications implicit functions implies indicated instance integrability conditions Inverse Problem Jacobi's equations kinematical form Lagrange's equations Lagrangian least class Legendre transform Lie algebra linear manifold matrix methodological necessary and sufficient Newtonian Mechanics Newtonian systems non-self-adjoint nonconservative nonlinear ordered direct analytic ordinary differential equations particles phase space physical Poincare Lemma potential proof R2n+ represent Santilli satisfies second-order Section significance star-shaped region sufficient conditions tensor theory variables variational approach variational forms vector velocities