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Full-Text Articles in Physical Sciences and Mathematics
Wheels On Wheels On Wheels-Surprising Symmetry, Frank A. Farris
Wheels On Wheels On Wheels-Surprising Symmetry, Frank A. Farris
Mathematics and Computer Science
While designing a computer laboratory exercise for my calculus students, I happened to sketch the curve defined by this vector equation: (x, y) = (cos(t), sin(t)) + 1/2(cos(7t), sin(7t)) + 1/3(sin(17t), cos(17t)). I was thinking of the curve traced by a particle on a wheel mounted on a wheel mounted on a wheel, each turning at a different rate. The first term represents the largest wheel, of radius 1, turning counter-clockwise at one radian per second. The second term represents a smaller wheel centered at the edge of the first, turning 7 times as fast. The third term is for …
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Doctoral Theses
No abstract provided.
The Inverse Problem Of The Calculus Of Variations For Scala Fourth Order Ordinary Differential Equations, Mark E. Fels
The Inverse Problem Of The Calculus Of Variations For Scala Fourth Order Ordinary Differential Equations, Mark E. Fels
Mark Eric Fels
A simple invariant characterization of the scalar fourth-order ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier are expressed in terms of the vanishing of two relative invariants which can be associated with any fourth-order equation through the application of Cartan's equivalence method. The solution to the inverse problem for fourth-order scalar equations provides the solution to an equivalence problem for second-order Lagrangians, as well as the precise relationship between the symmetry algebra of a variational equation and the divergence symmetry algebra of the associated Lagrangian.