How is the Coriolis generalized potential obtained

In summary, the Coriolis potential last term of (42) is obtained by integration through r and R from last term of (40), and there is no need to integrate through velocity since the Coriolis force already takes it into account.
  • #1
AlephClo
32
1
The Coriolis potential last term of (42) is obtained by integration through r and R from last term of (40).
I do not understand why we do not need to integrate through v as well, since the Coriolis force depends on v?

upload_2019-1-17_17-22-28-png.png

upload_2019-1-17_17-23-20-png.png


Homework Equations


Equation (41) is wrong I think, L must be replaced by U.
The forces for the 2 springs are F(r)= -kr, and F(R)= -kR (bold are vectors)
The generalized force Qj = Fi ⋅ δri/δqj (δ is del the partial derivative; j and i are indices)

The Attempt at a Solution


the 4 terms of (42) are obtainable from the intergration relatively to r and R.
Since the Coriolis force is dependent of the velocity v, why we do not need to Integration relative to v = (dr/dt, dR/dt) as well?

Or more generally when is it required that we integrate through position and velocity the force that depends on position and velocity to obtain a generalized potential.

Thank you.

 

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  • #2
The Coriolis force is a type of inertial force that depends on the velocity of the object. It is an effect of the Coriolis acceleration, which is caused by the rotation of the Earth. Therefore, there is no need to integrate through velocity for the Coriolis potential because it is already taken into account by the rotation of the Earth. However, if you were considering a different type of inertial force, such as a centrifugal force, then you would need to integrate both position and velocity in order to obtain the generalized potential.
 

Related to How is the Coriolis generalized potential obtained

1. How is the Coriolis generalized potential obtained?

The Coriolis generalized potential is obtained by solving the Navier-Stokes equations, which describe the motion of fluids. This involves considering the effects of the Earth's rotation on the fluid motion and incorporating the Coriolis force into the equations.

2. What is the significance of the Coriolis generalized potential?

The Coriolis generalized potential is significant because it helps explain the observed deflection of objects moving on the Earth's surface, such as winds and ocean currents. It also plays a crucial role in predicting weather patterns and ocean circulation.

3. How is the Coriolis generalized potential related to the Coriolis force?

The Coriolis generalized potential is directly related to the Coriolis force. The potential represents the potential energy associated with the Coriolis force, and is used to calculate the force acting on an object in motion.

4. Can the Coriolis generalized potential be calculated for any location on Earth?

Yes, the Coriolis generalized potential can be calculated for any location on Earth. The potential is dependent on the latitude and rotation rate of the Earth, which are constant values at any given location.

5. Are there any limitations to using the Coriolis generalized potential?

There are some limitations to using the Coriolis generalized potential. It assumes a steady state and does not account for other forces, such as friction, that may affect the motion of fluids. It also does not account for the Earth's topography, which can have an impact on fluid motion.

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