By Taeyoung Lee

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A simple definition. Riemann's integral of 1867 can be summarized as f (t)dt = lim f (τ i)(t i − t i−1). This summary conceals some of the complexity—for example, the limit is of a net, not a sequence—but it displays what we wish to emphasize: The integral is formed by combining the values f (τ i) in a very direct fashion. The values of f are used less(More)
This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on a manifold embedded in R n , which appears often in robotics and multi body dynamics. Euler–Lagrange equations and Hamilton's equations are developed in a coordinate-free fashion on a manifold, without relying on local parameterizations that may lead to(More)
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