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Walking is often modeled as an inverted pendulum system in which the center of mass vaults over the rigid stance limb. Running is modeled as a simple spring-mass system in which the center of mass… (More)
Abstract In this paper, we study the Green's function to find numerical solutions of second-order ordinary differential equations for two-point boundary value problems. We derive some properties of… (More)
Let Q be a compact, connected n-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If n 6= 3 is odd, or if π1(Q) is infinite, we show that the cosphere bundle of… (More)
The geodesic flow of a Riemannian metric on a compact manifold $Q$ is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action… (More)
We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a… (More)
The geodesic flow of a Riemannian metric on a compact manifold Q is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action on… (More)