Solving for Euler Angles
3
$begingroup$
I would like to determine Euler angles according to the following example.
My example:
I have the three vectors in an original set of axes:
r1e = {-0.517853, 0., -0.759239}
r2e = {-0.517853, 0., 0.759239}
r3e = {0.0647316, 0., 0.}
And after expressing them in a new reference frame they obtain the following components:
rt1e={0.310733, -0.358839, -0.786917}
rt2e={0.690333, 0.298661, 0.527983}
rt3e={-0.0625667, 0.00376111, 0.0161833}
In reality, I know the Euler angles to be $(30,60,120)$ degrees. How can I get Mathetmatica to give me this?
equation-solving rotation
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
$endgroup$
|
show 4 more comments
3
$begingroup$
I would like to determine Euler angles according to the following example.
My example:
I have the three vectors in an original set of axes:
r1e = {-0.517853, 0., -0.759239}
r2e = {-0.517853, 0., 0.759239}
r3e = {0.0647316, 0., 0.}
And after expressing them in a new reference frame they obtain the following components:
rt1e={0.310733, -0.358839, -0.786917}
rt2e={0.690333, 0.298661, 0.527983}
rt3e={-0.0625667, 0.00376111, 0.0161833}
In reality, I know the Euler angles to be $(30,60,120)$ degrees. How can I get Mathetmatica to give me this?
equation-solving rotation
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
$endgroup$
$begingroup$
Have you triedEulerAngles?
$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
1
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
1
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18
|
show 4 more comments
3
3
3
1
$begingroup$
I would like to determine Euler angles according to the following example.
My example:
I have the three vectors in an original set of axes:
r1e = {-0.517853, 0., -0.759239}
r2e = {-0.517853, 0., 0.759239}
r3e = {0.0647316, 0., 0.}
And after expressing them in a new reference frame they obtain the following components:
rt1e={0.310733, -0.358839, -0.786917}
rt2e={0.690333, 0.298661, 0.527983}
rt3e={-0.0625667, 0.00376111, 0.0161833}
In reality, I know the Euler angles to be $(30,60,120)$ degrees. How can I get Mathetmatica to give me this?
equation-solving rotation
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
$endgroup$
I would like to determine Euler angles according to the following example.
My example:
I have the three vectors in an original set of axes:
r1e = {-0.517853, 0., -0.759239}
r2e = {-0.517853, 0., 0.759239}
r3e = {0.0647316, 0., 0.}
And after expressing them in a new reference frame they obtain the following components:
rt1e={0.310733, -0.358839, -0.786917}
rt2e={0.690333, 0.298661, 0.527983}
rt3e={-0.0625667, 0.00376111, 0.0161833}
In reality, I know the Euler angles to be $(30,60,120)$ degrees. How can I get Mathetmatica to give me this?
equation-solving rotation
equation-solving rotation
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
edited Jan 6 at 18:29
Spherical Cow
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
asked Jan 6 at 17:59
Spherical CowSpherical Cow
162
162
$begingroup$
Have you triedEulerAngles?
$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
1
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
1
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18
|
show 4 more comments
$begingroup$
Have you triedEulerAngles?
$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
1
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
1
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18
$begingroup$
Have you tried
EulerAngles?$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
Have you tried
EulerAngles?$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
1
1
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
1
1
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18
|
show 4 more comments
1 Answer
1
active
oldest
votes
7
$begingroup$
As noted, you can use FindGeometricTransform in tandem with EulerAngles:
r = {{-0.517853, 0., -0.759239}, {-0.517853, 0., 0.759239}, {0.0647316, 0., 0.}};
rt = {{0.310733, -0.358839, -0.786917}, {0.690333, 0.298661, 0.527983},
{-0.0625667, 0.00376111, 0.0161833}};
fg = FindGeometricTransform[r, rt];
EulerAngles[Drop[TransformationMatrix[Last[fg]], -1, -1]]/°
{60.0048, 30.0019, 120.}
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
7
$begingroup$
As noted, you can use FindGeometricTransform in tandem with EulerAngles:
r = {{-0.517853, 0., -0.759239}, {-0.517853, 0., 0.759239}, {0.0647316, 0., 0.}};
rt = {{0.310733, -0.358839, -0.786917}, {0.690333, 0.298661, 0.527983},
{-0.0625667, 0.00376111, 0.0161833}};
fg = FindGeometricTransform[r, rt];
EulerAngles[Drop[TransformationMatrix[Last[fg]], -1, -1]]/°
{60.0048, 30.0019, 120.}
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
$endgroup$
add a comment |
7
$begingroup$
As noted, you can use FindGeometricTransform in tandem with EulerAngles:
r = {{-0.517853, 0., -0.759239}, {-0.517853, 0., 0.759239}, {0.0647316, 0., 0.}};
rt = {{0.310733, -0.358839, -0.786917}, {0.690333, 0.298661, 0.527983},
{-0.0625667, 0.00376111, 0.0161833}};
fg = FindGeometricTransform[r, rt];
EulerAngles[Drop[TransformationMatrix[Last[fg]], -1, -1]]/°
{60.0048, 30.0019, 120.}
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
$endgroup$
add a comment |
7
7
7
$begingroup$
As noted, you can use FindGeometricTransform in tandem with EulerAngles:
r = {{-0.517853, 0., -0.759239}, {-0.517853, 0., 0.759239}, {0.0647316, 0., 0.}};
rt = {{0.310733, -0.358839, -0.786917}, {0.690333, 0.298661, 0.527983},
{-0.0625667, 0.00376111, 0.0161833}};
fg = FindGeometricTransform[r, rt];
EulerAngles[Drop[TransformationMatrix[Last[fg]], -1, -1]]/°
{60.0048, 30.0019, 120.}
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
$endgroup$
As noted, you can use FindGeometricTransform in tandem with EulerAngles:
r = {{-0.517853, 0., -0.759239}, {-0.517853, 0., 0.759239}, {0.0647316, 0., 0.}};
rt = {{0.310733, -0.358839, -0.786917}, {0.690333, 0.298661, 0.527983},
{-0.0625667, 0.00376111, 0.0161833}};
fg = FindGeometricTransform[r, rt];
EulerAngles[Drop[TransformationMatrix[Last[fg]], -1, -1]]/°
{60.0048, 30.0019, 120.}
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
answered Jan 6 at 18:38
J. M. is computer-less♦J. M. is computer-less
96.3k10301461
96.3k10301461
add a comment |
add a comment |
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$begingroup$
Have you tried
EulerAngles?$endgroup$
– Henrik Schumacher
Jan 6 at 18:09
$begingroup$
That command won't work, as the rotation matrix itself is not known. Only the two vectors.
$endgroup$
– Spherical Cow
Jan 6 at 18:10
1
$begingroup$
In general, a rotation matrix is not uniquely defined by the action on a single vector...
$endgroup$
– Henrik Schumacher
Jan 6 at 18:12
$begingroup$
Fair enough, but in this case the problem has been constructed such that the three Euler angles are known to exist. The question specifically relates to why NSolve is not working.
$endgroup$
– Spherical Cow
Jan 6 at 18:14
1
$begingroup$
What I tried to say: If you prescribe a pair $u$ and $v$ of same length $neq 0$ in $mathbb{R}^3$, then there will be a one-parameter family of rotations (and thus a one-parameter family of Euler angles) that map $u$ to $v$. So, it is as it is: Your problem is underdetermined.
$endgroup$
– Henrik Schumacher
Jan 6 at 18:18