Accessible Points and Sub-Manifolds of Mechanical Systems. Controllability

Part of the Theoretical and Mathematical Physics book series (TMP)


In this chapter we study the question of whether or not two points m 0 and m 1 in the configuration space of a mechanical system can be connected by a trajectory. It is known (see, e.g., Hartman (1964)) that for a second order differential equation (i.e., in particular, for Newton’s law) on Euclidean space such a trajectory exists provided that the right-hand side of the differential equation is bounded and continuous. More precisely, for any two points m 0 and m 1 and any interval [a,b], there exists a solution m(t) such that m(a)=m 0 and m(b)=m 1. When the right-hand side is linearly bounded, some similar results are known for small time intervals.


Mechanical System Accessible Point Lower Semicontinuous Conjugate Point Complete Riemannian Manifold 
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  1. 144.
    Hartman, P.: Ordinary Differential Equations. John Wiley and Sons, N.Y.-L.-Sydney (1964) Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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