How to Derive the Simplified Form of Modified Euler Equations?

AI Thread Summary
To derive the simplified form of the modified Euler equations, the key step involves applying the quadratic formula to the equation M_x=(I_0-I)\dot\Psi^2\sin\theta\cos\theta+I_0\dot\Phi\dot\Psi\sin\theta. The goal is to isolate \dot\Psi, which can be achieved by rearranging the equation into a standard quadratic form. The simplification provided in the book can be reached by substituting the appropriate values and solving for \dot\Psi. This process highlights the importance of recognizing the quadratic nature of the equation. Understanding these steps is essential for successfully deriving the desired expression.
Telemachus
Messages
820
Reaction score
30

Homework Statement


Hi there. I'm not sure if this question corresponds to this subforum, but I think you must be more familiarized with it. The thing is I don't know how to get from:

M_x=(I_0-I)\dot\Psi^2\sin\theta\cos\theta+I_0\dot\Phi\dot\Psi\sin\theta

to:
\dot\Psi=\displaystyle\frac{I_0\dot\Phi}{2(I-I_0)\cos\theta} \left[1\pm \left( {1-\displaystyle\frac{4M_x(I-I_0)\cos\theta}{I_0^2\dot\Phi^2\sin\theta}}\right)^{1/2}\right]
I don't know how to get Phi from the first, but this is the simplification given on my book, but I don't know which intermediate steps to give.

Bye, and thanks.
 
Physics news on Phys.org
Looks like a pretty straightforward application of the quadratic formula to find Psi-dot.
 
Right. Thanks.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Back
Top