Recent content by wrobel

This is just to share some teaching experience. A problem about trajectory of a projectile in the atmosphere is very well known. The trajectory has a vertical asymptote. This fact is easy to obtain by using the stability theory. Consider equations of motion. Let ##\boldsymbol v=v_x\boldsymbol...

It looks like a question about reactions of ideal constraints. If it is so then yes reactions of the ideal constraints are calculated explicitly as functions of time, generalized velocities, and generalized coordinates.

15 Year Old Emma Kok Sings I have a question: Is this ok? Is this ok indeed?

I did not say that. Eventually this story is about definitions

I would say that average of a velocity on the time interval ##[t_1,t_2]## is equal to ##\frac{1}{t_2-t_1}\int_{t_1}^{t_2}\boldsymbol v(t)dt## provided nothing else is specified.

the tangent component of the acceleration of a point on the edge

I like David Morin. 8.27 is good for Lagrange equations.

You are said that the system moves so the friction force##=\mu N## "system's acceleration" is an unclear phrase by the way. A point can have acceleration.

https://en.wikipedia.org/wiki/Statically_indeterminate

In order for simplicity sake some authors make the narration harder. By definition the kinetic energy of a particle is ##T=\frac{m}{2}|\boldsymbol {\dot r}|^2=\frac{m}{2}(\boldsymbol {\dot r},\boldsymbol {\dot r}).## Thus we have ##\dot T=m(\boldsymbol {\dot r},\boldsymbol {\ddot...

The point of JimWhoKnew can be illustrated by the following simple analogy. Consider an initial value problem ##\dot x^2+x^2=1,\quad x(0)=0,\quad t\ge 0.## It has a solution ##x(t)=\sin t## for all ##t\ge 0##; and another solution ##x(t)=\sin t## for ##t\in[0,\pi/2]## and ##x(t)=1## for...

Bring the proofs please.