## Geometrical dynamics of certain nonlinear conservative systems with two degrees of freedom |

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### Contents

MOTION OF A PARTICLE ON AN ARBITRARY | 8 |

THE PROBLEM OF THE GENERALIZED DOUBLE | 27 |

MOTION UNDER THE INFLUENCE OF MULTIPLE | 68 |

4 other sections not shown

### Common terms and phrases

approximation Arbitrary Surface calculations centers of force Centers of Gravitation chapter class of two-degree-of-freedom complementary solution constant conventional dynamics cos0 cosh degrees of freedom determine differential equation differentiation with respect dynamical systems energy level equations of motion equipotential curve Euclidean plane Euler's Problem FIGURE fruit-stem system geometric equation geometrical dynamics Golden Delicious apple graphical construction Hence holonomic Hoop-Pendulum System initial slope integration isometric kinetic energy Lagrangian Legendre polynomials linear mode shapes linear normal mode linearized system modal line mode x Multiple Centers nonlinear normal modes nonlinear systems nonlinear vibrations normal modal curves normal mode vibrations obtains orbital equation out-of-phase parameters periodic orbit periodic solutions perturbational method perturbational procedure perturbational solution potential energy power series primes denote differentiation Problem of Three quadratic form Riemannian manifold right-hand side Rosenberg scleronomous conservative system Substituting tensor thesis Three Centers tion torsion springs total energy two-degree-of-freedom systems unit mass values zero