2025-02-28 08:55:42 +08:00
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Vector differentiation
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r = l dx
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A ^ p r/ p theta
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2025-02-28 16:17:25 +08:00
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partial derivative of r when observed from reference frame A with respect to theta
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p r/ p theta is meaningless if no frame is given!
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If theta, beta, alpah, l are all themselves functions of time
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-> theta(t), beta(t), alpha(t), l(t), time t is the single variable
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r(t) = a1(t)ax + a2(t)ay + a3(t)az
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A^ d r / dt = da1 / dt * ax + ...
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use dot notation
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when the measure numbers are expressions containing implict functions of time, eg theta(t), the chain role can be used to calculate the derivative.
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A ^ dr /dt = A ^ (p r / p theta) * (d theta / dt) + A ^ (p r / p beta) * (d beta / dt) + ...
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if t is explict in expressions 最后要加上 A ^ (p r / p t)
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Second (and higher) derivatives
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