Finding angular displacement from displacement vectors
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I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.
geometry trigonometry euclidean-geometry rotations
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
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add a comment |
$begingroup$
I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.
geometry trigonometry euclidean-geometry rotations
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
$endgroup$
add a comment |
$begingroup$
I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.
geometry trigonometry euclidean-geometry rotations
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
$endgroup$
I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.
geometry trigonometry euclidean-geometry rotations
geometry trigonometry euclidean-geometry rotations
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
edited Dec 7 '18 at 10:36
Appatakardot
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
asked Dec 6 '18 at 14:47
AppatakardotAppatakardot
11
11
add a comment |
add a comment |
1 Answer
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Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
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$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
$endgroup$
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
add a comment |
$begingroup$
Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
$endgroup$
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
add a comment |
$begingroup$
Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
$endgroup$
Hint:
The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.
Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
edited Dec 6 '18 at 21:08
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
answered Dec 6 '18 at 15:25
Emilio NovatiEmilio Novati
51.9k43474
51.9k43474
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
add a comment |
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
Could you explain it mathematically? what i am looking for is a mathematical expression which would help me solve for the angle
$endgroup$
– Appatakardot
Dec 6 '18 at 15:57
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
@Appatakardot I’ll just add that If you’re working with real-world noisy data and imprecise computations instead of mathematical ideals, then it’s quite likely that these bisectors won’t all meet in a single point, so you’ll have to estimate this intersection in some way.
$endgroup$
– amd
Dec 6 '18 at 19:52
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
$begingroup$
YES. I am working with real-world data which is why i am not satisfied with any of the responses i have received so far. If you have a suggestion on how i can approximate the angular displacement as accurately as possible. please indicate here
$endgroup$
– Appatakardot
Dec 7 '18 at 10:38
add a comment |
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