Robert S. Manning

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We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler–Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting(More)
The theory of conjugate points in the classic calculus of variations allows, for a certain class of functionals, the characterization of a critical point as stable (i.e., a local minimum) or not. In this work, we generalize this theory to more general functionals, assuming certain generic properties of the second variation operator. The extended conjugate(More)
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