Multi-time Euler-Lagrange dynamics
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Section 1 underlines the limitations of standard multi-variable variational calculus and the sense of multitime. Section 1 formulates the controllability problem for a multiple integral functional or for a path independent curvilinear integral subject to a multitime evolution of flow type. Section 2 describes a two-time optimal economic growth modelled by Euler-Lagrange PDEs associated to a double integral functional or to a path independent curvilinear integral in two dimensions. Section 3 motivates the optimal economic growth by two-time maximum principles. Section 4 studies the two-time optimal economic growth with bang-bang policy based on a curvilinear integral action.