Functional Differential Geometry

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The metric for a unit sphere, expressed in colatitude and longitude , is

Compute the Lagrange equations for motion of a free particle on the sphere …

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(define((L2 mass metric)place velocity)(* 1/2 mass((metric velocity velocity)place)))(define((Lc mass metric coordsys)state)(let((x(coordinates state))(v(velocities state))(e(coordinate-system->vector-basis coordsys)))((L2 mass metric)((point coordsys)x)(* e v))))(definethe-metric(literal-metric 'g R2-rect))(defineL(Lc 'm the-metric R2-rect))(L(up 't(up 'x 'y)(up 'vx 'vy)))(show-expression(L(up 't(up 'x 'y)(up 'v_x 'v_y))))

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(show-expression(L(up 't(up 'theta 'phi)(up 'thetadot 'phidot))))

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When and ,

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— Me@2022-10-27 10:30:50 AM

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2022.10.28 Friday (c) All rights reserved by ACHK

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