Determination of angle of deviation and rotation of the vector












0












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I'm sorry for my drawing skills and mistakes in grammar.



I'm trying to solve next task:



Phone is somehow fixed in a phoneholder in a car. As it is displayed on picture. Purple - car coordinate system, red - phone's one.



X - perpendicular to the movement and parallel to the ground
Y - parallel to the movement and to the ground
Z - perpendicular to the ground


During the calibration phase I can assume, that all measured acceleration belongs to single axis - Y. So I have two vectors:



Measured acceleration (ma) - [x, y, z]
Expected acceleration (ea) - [0, |ma|, 0]


How can I calculate rotation matrix, angles or something else I don't know about, to transform measured (phone) acceleration to expected (car)?



example










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  • $begingroup$
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
    $endgroup$
    – José Carlos Santos
    Dec 3 '18 at 10:04










  • $begingroup$
    You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
    $endgroup$
    – amd
    Dec 4 '18 at 3:42
















0












$begingroup$


I'm sorry for my drawing skills and mistakes in grammar.



I'm trying to solve next task:



Phone is somehow fixed in a phoneholder in a car. As it is displayed on picture. Purple - car coordinate system, red - phone's one.



X - perpendicular to the movement and parallel to the ground
Y - parallel to the movement and to the ground
Z - perpendicular to the ground


During the calibration phase I can assume, that all measured acceleration belongs to single axis - Y. So I have two vectors:



Measured acceleration (ma) - [x, y, z]
Expected acceleration (ea) - [0, |ma|, 0]


How can I calculate rotation matrix, angles or something else I don't know about, to transform measured (phone) acceleration to expected (car)?



example










share|cite|improve this question











$endgroup$












  • $begingroup$
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
    $endgroup$
    – José Carlos Santos
    Dec 3 '18 at 10:04










  • $begingroup$
    You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
    $endgroup$
    – amd
    Dec 4 '18 at 3:42














0












0








0





$begingroup$


I'm sorry for my drawing skills and mistakes in grammar.



I'm trying to solve next task:



Phone is somehow fixed in a phoneholder in a car. As it is displayed on picture. Purple - car coordinate system, red - phone's one.



X - perpendicular to the movement and parallel to the ground
Y - parallel to the movement and to the ground
Z - perpendicular to the ground


During the calibration phase I can assume, that all measured acceleration belongs to single axis - Y. So I have two vectors:



Measured acceleration (ma) - [x, y, z]
Expected acceleration (ea) - [0, |ma|, 0]


How can I calculate rotation matrix, angles or something else I don't know about, to transform measured (phone) acceleration to expected (car)?



example










share|cite|improve this question











$endgroup$




I'm sorry for my drawing skills and mistakes in grammar.



I'm trying to solve next task:



Phone is somehow fixed in a phoneholder in a car. As it is displayed on picture. Purple - car coordinate system, red - phone's one.



X - perpendicular to the movement and parallel to the ground
Y - parallel to the movement and to the ground
Z - perpendicular to the ground


During the calibration phase I can assume, that all measured acceleration belongs to single axis - Y. So I have two vectors:



Measured acceleration (ma) - [x, y, z]
Expected acceleration (ea) - [0, |ma|, 0]


How can I calculate rotation matrix, angles or something else I don't know about, to transform measured (phone) acceleration to expected (car)?



example







linear-algebra linear-transformations






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 3 '18 at 10:11







Zwei

















asked Dec 3 '18 at 9:55









ZweiZwei

1011




1011












  • $begingroup$
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
    $endgroup$
    – José Carlos Santos
    Dec 3 '18 at 10:04










  • $begingroup$
    You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
    $endgroup$
    – amd
    Dec 4 '18 at 3:42


















  • $begingroup$
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
    $endgroup$
    – José Carlos Santos
    Dec 3 '18 at 10:04










  • $begingroup$
    You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
    $endgroup$
    – amd
    Dec 4 '18 at 3:42
















$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Dec 3 '18 at 10:04




$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Dec 3 '18 at 10:04












$begingroup$
You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
$endgroup$
– amd
Dec 4 '18 at 3:42




$begingroup$
You have enough information to determine the true $Y$-axis direction, but not enough to determine which way is “up.”
$endgroup$
– amd
Dec 4 '18 at 3:42










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