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Preamble GENERALITIES AND TYPICAL PROBLEMS
Mathematics and to Space Science
Statement of the Simplest Problem and Some Cognate Matters
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admissible curves boundary bounded calculus of variations canonical Chapter clearly completes the proof consists constant continuous function continuously differentiable convergence convex function corresponding defined definition deformation denote derivative differential equation domain dual elementary equivalent Euclidean Euclidean space Euler equation existence theory expression extremal arc finite number fixed follows function x(t further geodesic given Hamiltonian Hence Hilbert homogeneous hyperplane inequality infimum initial values integral integrand intersection interval Lagrange brackets Lagrange problem Lagrangian lemma length limit line element linear function mathematics matrix maximum principle minimum Moreover neighborhood nonparametric nonsingular notion optimal control origin pair parametric polygonal flow positive cone reader rectifiable curve relation relevant representation restriction Riesz measure satisfy scalar secondary segment sequence simply smooth solution space subset suppose supremum suspected optimal tangent term theorem trajectory uniformly vanishes variables variational problem vector verify vertex write x-space z-space