borish
May20-08, 03:12 PM
Describing the a model
Two hands of an analog clock: r1 (hand of the minutes) and r2 (hand of the hours),
and a relative vector r21 between them.
The question:
In spherical harmonics representation how can I describe the motion of the vector r21 by the rotation of r1 relative to r2 (r2 is fixed).
Direction:
I would like to describe the first rank spherical harmonics of r21 -> \Upsilon^{1}_{k(m,n)}(r21) by the product of the two spherical harmonics r1 -> \Upsilon^{1}_{m}(\theta_{1},\varphi_{1})
and r2 -> \Upsilon^{1}_{n}(\theta_{2},\varphi_{2})
somthing like ~ \Upsilon^{1}_{m}(\theta_{1},\varphi_{1})\otimes\Upsilon^{1}_{n}(\theta_{2},\varphi_{2}).
Should I use the bipolar harmonics ? I don't realy understand this formula.
Thank
Two hands of an analog clock: r1 (hand of the minutes) and r2 (hand of the hours),
and a relative vector r21 between them.
The question:
In spherical harmonics representation how can I describe the motion of the vector r21 by the rotation of r1 relative to r2 (r2 is fixed).
Direction:
I would like to describe the first rank spherical harmonics of r21 -> \Upsilon^{1}_{k(m,n)}(r21) by the product of the two spherical harmonics r1 -> \Upsilon^{1}_{m}(\theta_{1},\varphi_{1})
and r2 -> \Upsilon^{1}_{n}(\theta_{2},\varphi_{2})
somthing like ~ \Upsilon^{1}_{m}(\theta_{1},\varphi_{1})\otimes\Upsilon^{1}_{n}(\theta_{2},\varphi_{2}).
Should I use the bipolar harmonics ? I don't realy understand this formula.
Thank