[yt-users] Angular momentum with a general axis

[Matthew Turk]

Hi Junhwan,

On Wed, Jun 4, 2014 at 1:54 PM, Junhwan Choi (최준환)
<choi.junhwan at gmail.com> wrote:
> On Wed, Jun 4, 2014 at 11:20 AM, Matthew Turk <matthewturk at gmail.com> wrote:
>> Hi Junhwan,
>>
>> On Tue, Jun 3, 2014 at 10:38 PM, Junhwan Choi (최준환)
>> <choi.junhwan at gmail.com> wrote:
>>> Hi yt users,
>>>
>>> I wrote basic yt script to make Jz profile of my simulation as follow:
>>> ======
>>> import matplotlib as matplotlib
>>> matplotlib.use('Agg')
>>> from yt.mods import *
>>> import matplotlib.pyplot as plt
>>>
>>> Nbin = 75
>>> rmax = 1200 # in pc
>>> index = 60
>>>
>>> pf = load("../DD%04d/DD%04d" % (index,index))
>>> rmin = [1e-4,2.0*pf.h.get_smallest_dx()*pf.units['pc']]
>>> sphere = pf.h.sphere(center, (rmax, 'pc'))
>>> bulk_velocity = sphere.quantities['BulkVelocity']()
>>> sphere.set_field_parameter('bulk_velocity', bulk_velocity)
>>>
>>> profile = BinnedProfile1D(sphere, Nbin, "Radiuspc", max(rmin), rmax,
>>> log_space=True, lazy_reader=True, end_collect=False)
>>> profile.add_fields('AngularMomentumZ',weight=None)
>>> profile.add_fields('Radius',weight=None)
>>>
>>> plt.loglog(profile['Radiuspc'],
>>> profile['AngularMomentumZ'],label='t=%4.2fMyr' %
>>> (pf.current_time*7.26), linestyle="-",color='b')
>>> plt.xlabel('r [pc]')
>>> plt.ylabel(r'j ($\rm{cm}^2/\rm{s}$)',fontsize=17)
>>> plt.xlim(1e-4,1000)
>>> plt.legend(loc=4, prop={'size':10})
>>> plt.savefig('jprof2K_%04d' % index)
>>> =========
>>>
>>> Now I would like to compute the AngularMomentum not according to x,
>>> y,and z but according to a general axis (i.e. angular momentum axis).
>>> Is there any simple way in yt to compute the AngularMomentum according
>>> to the general axis?
>>
>> My reading of this is that what you want to do is compute:
>>
>> L = r [x] mv
>>
>> (provided by yt) and then compute your final L vector as:
>>
>> L' = L [x] mv
>>
>> is that right?  This would then be:
>>
>> (r [x] mv) [x] mv
>>
>> which I'm not really sure is what you're looking for, right?  Can you
>> describe your desired result in vector notation?
>>
> I would like to compute the L_{rot} means the angular momentum
> regarding to rotating axis.
> Hence, what I am looking for as in vector notation would be the following.
> First (as you think), compute L as
>
> L = r[x]mv
>
> and compute the rotation matrix (Omega) that satisfies
>                              | 0 |
> Omega odot L/|L| = | 0 |
>                              | 1 |
>
> [Means the rotation matrix that rotate L vector to (0,0,1)]
> and compute
>
> L' = (Omega odot r) [x] (Omega odot mv)
>
> From L', I can get L'_z that is L_{rot}.
>

Does this help?

http://planetmath.org/rotationalinvarianceofcrossproduct

My reading is that if you have a proper rotation matrix for Omega, L'
= Omega odot L.

-Matt

> Thank you,
> Junhwan
> _______________________________________________
> yt-users mailing list
> yt-users at lists.spacepope.org
> http://lists.spacepope.org/listinfo.cgi/yt-users-spacepope.org