## Foundations of theoretical mechanics: the inverse problem in Newtonian mechanics |

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### Contents

ElementaI Mathematics | 15 |

VariationaI Approach to SeIfAdjointness | 54 |

The FundamentaI AnaIytic Theorems | 110 |

Copyright | |

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### Common terms and phrases

acting forces adjoint system admissible analysis arbitrary 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 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 forces Newtonian Mechanics Newtonian systems non-self-adjoint nonconservative nonlinear ordered direct analytic ordinary differential equations particles phase space physical Poincare Lemma potential proof R2n+1 of points region R2n+1 represent Santilli satisfies second-order Section significance star-shaped region sufficient conditions tensor theory variables variational approach variational forms vector velocities