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Conjugate points in the Euler elastic problem. (English) Zbl 1203.49005
Summary: For the classical Euler elastic problem, conjugate points are described. Inflexional elasticas admit the first conjugate point between the first and third inflexion points. All other elasticas do not have conjugate points. As a result, the problem of stability of Euler elasticas is solved.
Reviewer: Reviewer (Berlin)

MSC:
49J15 Existence theories for optimal control problems involving ordinary differential equations
49Q10 Optimization of shapes other than minimal surfaces
93C10 Nonlinear systems in control theory
74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65D07 Numerical computation using splines
74G60 Bifurcation and buckling
74G65 Energy minimization in equilibrium problems in solid mechanics
Software:
Mathematica
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