lengths of plane curves
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4 matching pages
1: 19.30 Lengths of Plane Curves
§19.30 Lengths of Plane Curves
►§19.30(i) Ellipse
… ►§19.30(ii) Hyperbola
… ►§19.30(iii) Bernoulli’s Lemniscate
…2: 22.18 Mathematical Applications
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§22.18(i) Lengths and Parametrization of Plane Curves
…3: 1.6 Vectors and Vector-Valued Functions
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►then the length of a path for is
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►The geometrical image of a path is called a simple
closed curve if is one-to-one, with the exception .
The curve
is piecewise differentiable if is piecewise differentiable.
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►and be the closed and bounded point set in the
plane having a simple closed curve
as boundary.
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4: 28.33 Physical Applications
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►We shall derive solutions to the uniform, homogeneous, loss-free, and stretched elliptical ring membrane with mass per unit area, and radial tension per unit arc length.
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►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as .
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►As runs from to , with and fixed, the point moves from to along the ray given by the part of the line that lies in the first quadrant of the -plane.
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►For points that are at intersections of with the characteristic curves
or , a periodic solution is possible.
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