## Tensor Calculus and Analytical DynamicsTensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form. |

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### Contents

Introduction and Background brief history algebraic preliminaries | 20 |

Tensor Algebra | 32 |

Tensor Analysis | 93 |

MetricEquipped Manifolds | 115 |

Introduction to Analytical Dynamics | 169 |

Introduction to Analytical Dynamics | 170 |

RAISON DETRE AND SOME EDUCATIONAL | 178 |

Chapter 5 | 181 |

Chapter 6 | 233 |

Kinetics | 285 |

A notable exception being the masterly but brief and not too readable by nonmathematicians account | 312 |

371 | |

### Common terms and phrases

absolute absolute vectors acceleration affinities antisymmetric axes calculus Christoffels coefficients configuration space constant constraint reaction contravariant components contravariant vector corresponding covariant derivatives curl curvature curve curvilinear coordinates d(dQK defined definition displacement vector dr/dt dynamics equations of motion Euclidean space Example forces frame Frobenius functions fundamental geometrical gradient Hamel holonomic variables independent indices inertial integrability invariant invoking Equation kinematical kinetic kinetostatic Lagrangean linear manifold mechanics metric tensor Newton-Euler nonholonomic variables normal notation obtain orthogonal orthonormal parallel transport particle perturbation Pfaffian constraints physical plane Problem Quotient Rule recalling Equations rectangular Cartesian coordinates relative Ricci's lemma Riemannian rigid body scalar scleronomic similarly surface symmetric tangent theorem torsionless transformation transitivity equations unconstrained vanish vector space velocity virtual displacement yields