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  1. K

    A Virtual work in Atwood's machine

    OK, thanks. I was confused by the remark "This trivial problem emphasizes that the forces of constraint--here the tension in the rope--appear nowhere in the Lagrangian formulation." Let's say I want to be extremely formal. How would I proceed? The constraint is ##x_1+x_2=l##, where ##x_i## is...
  2. K

    A Virtual work in Atwood's machine

    The first chapter in Goldstein's Classical Mechanics ends with 3 examples about how to apply Lagrange's eqs. to simple problems. The second example is about the Atwood's machine. The book says that the tension of the rope can be ignored, but I don't understand why. The two masses can move...
  3. K

    A Euler's Principal Axis

    You're probably thinking about the eigendecomposition of the inertia matrix. This is something unrelated to that. Here's the lecture: It turns out we're assuming that ##\boldsymbol\omega## is parallel to the principal axis ##\hat{\boldsymbol e}## so, by the transport theorem, the inertial...
  4. K

    A Euler's Principal Axis

    When we solve Euler's differential equations for rigid bodies we find the angular acceleration ##\dot{\boldsymbol\omega}## and then the angular velocity ##\boldsymbol\omega##. Integrating ##\boldsymbol\omega## is less straightforward, so we start from a representation of the attitude, take its...
  5. K

    A On Newton's first and second laws

    ... or your reference frame is not inertial, as in this case.
  6. K

    A On Newton's first and second laws

    That's because of gravity and friction. If you remove all forces, my acceleration won't be 0 in that frame.
  7. K

    A On Newton's first and second laws

    Thank you all for your answers. As for QM I don't think I'll ever learn about it as I'm learning Mechanics to better understand underactuated robotics and locomotion in particular.
  8. K

    A On Newton's first and second laws

    Any example?
  9. K

    A On Newton's first and second laws

    According to Scheck's definition, inertial frames are frames with respect to which Newton's first law has analytic form ##\ddot{\pmb{r}}(t)=0##.
  10. K

    A On Newton's first and second laws

    I'm reading Scheck's book about Mechanics and it says that Newton's first law is not redundant as it defines what an inertial system is. My problem is that we could say the same about Newton's second law. Indeed, Newton's second law is only valid, in general, for inertial systems, so it also...
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