11:13 while you're writing the kinetic energy due to the velocity of the bar at it's com, why you wrote the velocity directly "xdot + Vtangantial" I mean you added them up directly but they are vectors. Isnt the correct way to do that is adding the squares of them together?
Hi. They are vectors, but the i and e_1 directions are not orthogonal. When e_1 is written in terms of i and j, and the resulting expression for v_G is linearized, the magnitude of v_G simply becomes (xdot + (ell*thetadot)/2). You could also find the squared magnitude of v_G and *then* linearize, but you would find the same result.
@@quinndd I was wrong about the square summation part since they are not orthogonal but my point was shouldnt we use cosine formula to find the resultant force? or basically we can write the kinetic energies due to both xdot and ell*thetadot/2 seperately. this looks correct but the result is different
@@ersinortagenc1367 In general, yes you are correct. However, since we are determining the linearized equations of motion, the cos(theta) term is approximately 1, while the sin(theta) term is approximately theta. As a result the velocity of G becomes v_G ~ (xdot + ell*thetadot/2) i while the j component vanishes.
Because the pin point B is accelerating, the summed moments about that point does not equal to I_B*alpha. In this case you can only take moments about the mass center, unless to add additional terms to the angular momentum balance equations.
Thanks a lot for your video...it's nice to think that they are great teachers in this world...mine where not so good
Thanks for watching, and I'm glad you found it helpful :)
11:13 while you're writing the kinetic energy due to the velocity of the bar at it's com, why you wrote the velocity directly "xdot + Vtangantial" I mean you added them up directly but they are vectors. Isnt the correct way to do that is adding the squares of them together?
Hi. They are vectors, but the i and e_1 directions are not orthogonal. When e_1 is written in terms of i and j, and the resulting expression for v_G is linearized, the magnitude of v_G simply becomes (xdot + (ell*thetadot)/2). You could also find the squared magnitude of v_G and *then* linearize, but you would find the same result.
@@quinndd I was wrong about the square summation part since they are not orthogonal but my point was shouldnt we use cosine formula to find the resultant force? or basically we can write the kinetic energies due to both xdot and ell*thetadot/2 seperately. this looks correct but the result is different
@@ersinortagenc1367 In general, yes you are correct. However, since we are determining the linearized equations of motion, the cos(theta) term is approximately 1, while the sin(theta) term is approximately theta. As a result the velocity of G becomes v_G ~ (xdot + ell*thetadot/2) i while the j component vanishes.
Of course. When you think about it it is like that. Thanks for your replay.
Great lecture thanks a lot
Why it is not moment of inertia about pin point?
Because the pin point B is accelerating, the summed moments about that point does not equal to I_B*alpha. In this case you can only take moments about the mass center, unless to add additional terms to the angular momentum balance equations.
Thank you for materials. Video is a very valuable. Can you write some literature about mass and "k" matrix?
Hi. This lecture has some additional information about how to identify Mass and Stiffness matrices < ua-cam.com/video/Lcjw9q1y-jg/v-deo.html >.