## Nonlinear stability of geometrically exact rods by the energy-momentum methodMathematical Sciences Institute, Cornell University, 1988 - 154 pages |

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### Contents

SlMO T A POSBErGH | 2 |

The Rigid Body 2 | 14 |

4 Equilibria of Geometrically Exact Rod Models | 21 |

5 other sections not shown

### Common terms and phrases

AJ(ze angular momentum associated assume axis block diagonal Casimir center of mass characterization compute configuration manifold corresponding momentum map cotangent bundle cotangent space critical points defined denote elasticity tensor energy-Casimir method energy-momentum functional energy-momentum method equations exact rod models extended inertia dyadic formal stability free boundary conditions G R3 geometrically exact rod given group action Hamiltonian Hamiltonian vector field infinitesimal rigid body J. C. SiMo J(ze Jacobi's identity ker[T Krishnaprasad & Marsden Krishnaprasad 1988 Legendre transformation Lemma Lie algebra line of centroids linear momentum method obtain orbit Pa<p phase space positive definite Proof proposition 2.1 quotient space Recall reduced phase space restricted result rigid body motions second variation spatial stored energy function stress free boundary superposed infinitesimal rigid symplectic symplectic manifolds tangent space TPrig TPrjg transverse axial rotation uniform rotation Vu-Quoc W^Ig Wjug Wriq Wrjg