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I need some help,...
On the surface of the Earth a cartesian coordinate system _E will be installed at the latitude ϕ. The axes of the coordinate system are aligned as following:
_x1-axis: points up
_x2-axis: points north
_x3-axis: points east
The underscores in front of the variables are a reminder that these variables relate to the non-inertalsystem _E.
The exercise I should solve asks the question:
How does the coriolis force depend on the latitude?
In the book I read, the coriolis force was deduced to the following formula:
_Fc = -2*m*(w x _r')
(two times the mass multiplied with the cross product of the angular velocity with the derivative of the position vektor, where the position vector is relating to the _E-system)
Now my problem:
Isn't there something missing in this formula? Because as I understand the coriolis force, the distance of the motion to the axis of rotation is of importance when calculating the coriolis force. But in this formula above, the position vector relates to the _E-system, so the distance to the axis of rotation is nowhere to be found in the formula.
The result as it reads in the book:
_Fc = -2*m*w*(_x3'*cos(ϕ) - _x2'*sin(ϕ), _x1'*sin(ϕ), -x1'*cos(ϕ))
where
_r = (_x1, _x2, _x3)
Can somebody explain to how I must understand this exercise. I'm pretty sure the book is correct. What am I missing? I really would appreciate any help...
--edit
sorry, missed the right subforum for this thread
On the surface of the Earth a cartesian coordinate system _E will be installed at the latitude ϕ. The axes of the coordinate system are aligned as following:
_x1-axis: points up
_x2-axis: points north
_x3-axis: points east
The underscores in front of the variables are a reminder that these variables relate to the non-inertalsystem _E.
The exercise I should solve asks the question:
How does the coriolis force depend on the latitude?
In the book I read, the coriolis force was deduced to the following formula:
_Fc = -2*m*(w x _r')
(two times the mass multiplied with the cross product of the angular velocity with the derivative of the position vektor, where the position vector is relating to the _E-system)
Now my problem:
Isn't there something missing in this formula? Because as I understand the coriolis force, the distance of the motion to the axis of rotation is of importance when calculating the coriolis force. But in this formula above, the position vector relates to the _E-system, so the distance to the axis of rotation is nowhere to be found in the formula.
The result as it reads in the book:
_Fc = -2*m*w*(_x3'*cos(ϕ) - _x2'*sin(ϕ), _x1'*sin(ϕ), -x1'*cos(ϕ))
where
_r = (_x1, _x2, _x3)
Can somebody explain to how I must understand this exercise. I'm pretty sure the book is correct. What am I missing? I really would appreciate any help...
--edit
sorry, missed the right subforum for this thread
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