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    Relativity: Differential Geometry

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    A particle moves along a parametrized curve given by

    x(lamda)=cos(lamda), y(lamda)=sin(lamda), z(lamda)=lamda

    Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
    where x = rsin(theta)cos(pheta)
    y=rsin(theta)sin(pheta)
    z=rcos(theta)
    so that the metric is
    ds^2=dr^2+(r^2)d(theta)^2+(r^2)sin^2(theta)d(pheta)^2

    Calculate the components of the tangent vector to the curve in both Cartesian and spherical polar coordinate systems.

    © BrainMass Inc. brainmass.com October 9, 2019, 8:20 pm ad1c9bdddf
    https://brainmass.com/math/differential-geometry/relativity-differential-geometry-147380

    Solution Summary

    This solution shows step-by-step calculations to express the path of the curve in the specific spherical polar coordinates and also determines the components of the tangent vector to the curve in both Cartesian and spherical polar coordinates. All workings and formulas are shown in a clear and structured manner.

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