- #1
thechunk
- 11
- 0
Is anyone familiar with the derivation for this formula for torsion.
[tex] \tau = \frac {\left( \begin{array}{ccc} \dot{x} & \ddot{x} & \dddot{x}\\\dot{y}& \ddot{y}& \ddot{y} \\\dot{z} & \ddot{z} & \dddot{z}\end{array} \right)} {|v \times a|^2}[/tex]
I know of expressing torsion as [tex]\tau = -\frac {dB} {dS} \cdot N [/itex], but I do not know how to derive the former. My teacher said it could be derived with knowledge from our multivariable class however my textbook reads that the derivation is found in more advanced texts. The numerator in the first formula looks like [tex](v \times a) \cdot a' [/itex], but I do not know where to go from there. Any ideas?[/tex][/tex]
[tex] \tau = \frac {\left( \begin{array}{ccc} \dot{x} & \ddot{x} & \dddot{x}\\\dot{y}& \ddot{y}& \ddot{y} \\\dot{z} & \ddot{z} & \dddot{z}\end{array} \right)} {|v \times a|^2}[/tex]
I know of expressing torsion as [tex]\tau = -\frac {dB} {dS} \cdot N [/itex], but I do not know how to derive the former. My teacher said it could be derived with knowledge from our multivariable class however my textbook reads that the derivation is found in more advanced texts. The numerator in the first formula looks like [tex](v \times a) \cdot a' [/itex], but I do not know where to go from there. Any ideas?[/tex][/tex]