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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Series Solutions, Factorials, And The Gamma Function, Steven J. Wilson
Series Solutions, Factorials, And The Gamma Function, Steven J. Wilson
Topics in Mathematics
Using a power series to solve an ordinary differential equation will often result in a solution whose general term involves a product of terms from an arithmetic sequence. This paper explores how factorials and the gamma function can be used to rewrite such general terms in a closed form.
Robot Space Coordinate Representation Of Objects In Euclidean Space, Justin Gallagher
Robot Space Coordinate Representation Of Objects In Euclidean Space, Justin Gallagher
Mathematical Sciences Technical Reports (MSTR)
Robot motion control strategies generally center around trajectory planning schemes which are point-to-point. This paper explores the problem of planning robot trajectories which sweep an area in a two-link robot's work space. A diffeomorphism which transforms the linear coordinates of Euclidean space to the non-linear angular coordinates which represent the displacements of the joint motors is developed. It is used to determine the distortion of an object's area at different locations in the robot's work space and for different robot link length geometries. Study of such distortions may lead to an optimization scheme by which the placement of the object …