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Full-Text Articles in Engineering
Formulation Of Integral Equations Using Analytic Green's Functions In Elliptic Cylindrical And Prolate Spheroidal Coordinates, Adam Schreiber
Formulation Of Integral Equations Using Analytic Green's Functions In Elliptic Cylindrical And Prolate Spheroidal Coordinates, Adam Schreiber
All Theses
It is desired to develop and present techniques, using analytic Green's functions in elliptic cylindrical coordinates and in prolate spheroidal coordinates, for formulating integral equations for physically practicable structures and sources. Equivalent models for two structures are introduced which serve as guides in the derivation of analytic Greens functions, comprising special functions and satisfying required boundary conditions. Expressions for needed field components are represented in terms of integrals of Greens functions times unknowns, and integral equations follow from the proper relationships among sources and field components needed to satisfy Maxwell's equations.
Derivation And Application Of A Conserved Orbital Energy For The Inverted Pendulum Bipedal Walking Model, Jerry E. Pratt, Sergey V. Drakunov
Derivation And Application Of A Conserved Orbital Energy For The Inverted Pendulum Bipedal Walking Model, Jerry E. Pratt, Sergey V. Drakunov
Publications
We present an analysis of a point mass, point foot, planar inverted pendulum model for bipedal walking. Using this model, we derive expressions for a conserved quantity, the “Orbital Energy”, given a smooth Center of Mass trajectory. Given a closed form Center of Mass Trajectory, the equation for the Orbital Energy is a closed form expression except for an integral term, which we show to be the first moment of area under the Center of Mass path. Hence, given a Center of Mass trajectory, it is straightforward and computationally simple to compute phase portraits for the system. In fact, for …