Surface transformations and their dynamical applications
Acta Mathematica1922Vol. 43(0), pp. 1–119
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Abstract
A state of motion in a dynamical system with two degrees of freedom depends on two space and two velocity coiirdinates, and thus may be represented by means of a point in space of four dimensions. When only those motions are considered which correspond to a given value of the energy constant, the points lie in a certain three-dimensional manifold. The motions are given as curves in this manifold. One such curve passes through each point.
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