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