fix dcm diff error

[zhouzq-thu]

References to other Issues or PRs

Fix ReferenceFrame DCM diff error #16824

Brief description of what is fixed or changed

Fix angular velocity from time differentiating the DCM.

from sympy import symbols
from sympy.physics.mechanics import ReferenceFrame, dynamicsymbols

q1, q2, q3 = dynamicsymbols('q1:4')

N = ReferenceFrame('N')
A = N.orientnew('A', 'axis', [q1, N.x])
B = A.orientnew('B', 'axis', [q2, A.y])
C = B.orientnew('C', 'axis', [q3, B.z])

DCM = C.dcm(N).T

D = N.orientnew('D', 'DCM', DCM)

print('DCM diff:', D.dcm(N) - C.dcm(N))
print('ang vel diff:', (D.ang_vel_in(N) - C.ang_vel_in(N)).simplify().express(N))

Result:

DCM diff: Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
ang vel diff: 0

Other comments

Release Notes

• physics.vector
  • fix ReferenceFrame _w_diff_dcm method

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• physics.vector
  • fix ReferenceFrame _w_diff_dcm method (#16828 by @zhouzq-thu)

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Fix ReferenceFrame DCM diff error #16824 

#### Brief description of what is fixed or changed

Fix angular velocity from time differentiating the DCM.

```
from sympy import symbols
from sympy.physics.mechanics import ReferenceFrame, dynamicsymbols

q1, q2, q3 = dynamicsymbols('q1:4')

N = ReferenceFrame('N')
A = N.orientnew('A', 'axis', [q1, N.x])
B = A.orientnew('B', 'axis', [q2, A.y])
C = B.orientnew('C', 'axis', [q3, B.z])

DCM = C.dcm(N).T

D = N.orientnew('D', 'DCM', DCM)

print('DCM diff:', D.dcm(N) - C.dcm(N))
print('ang vel diff:', (D.ang_vel_in(N) - C.ang_vel_in(N)).simplify().express(N))
```

Result:

```
DCM diff: Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
ang vel diff: 0
```


#### Other comments


#### Release Notes

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on how to write release notes. The bot will check your release notes
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<!-- BEGIN RELEASE NOTES -->

* physics.vector
  * fix ReferenceFrame ```_w_diff_dcm``` method

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[codecov]

Codecov Report

Merging #16828 into master will increase coverage by 0.014%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##            master    #16828       +/-   ##
=============================================
+ Coverage   73.849%   73.864%   +0.014%     
=============================================
  Files          619       619               
  Lines       159669    159712       +43     
  Branches     37476     37486       +10     
=============================================
+ Hits        117915    117970       +55     
+ Misses       36294     36281       -13     
- Partials      5460      5461        +1

[oscarbenjamin]

This looks reasonable although I haven't checked the calculation in detail. Was it just a bug in the formula?

Can you add a test for this? The example from #16824 could be added to sympy/physics/vector/tests/test_frame.py

[zhouzq-thu]

@oscarbenjamin, the test function has been added. Please check it.

Two test functions test_w_diff_dcm1() and test_w_diff_dcm2() both can be passed now.

[oscarbenjamin]

Can you also include explicitly what this is testing for rather than just comparing the output of two different functions?

Otherwise this test will pass even if both just output e.g. zero.

[zhouzq-thu]

I have added some documentation for both test functions and rewritten the original test_w_diff_dcm1() since it looks not good.

[oscarbenjamin]

Thanks!