Computational and Applied Mathematics Discussion Group September 23 2020, 1:39 amHi pips! Can someone help me with this question:
A particle of mass m moves in R3 under a central force F(r) = −dV/dr , in spherical coordinates, so (x, y, z) = (r cos(φ) sin(θ), r sin(φ) sin(θ), r cos(θ)).
Find the Lagrangian from first principles, in terms of (r, θ, φ) and their time derivatives.
(a) show that h, defined by h = mr2φ˙ sin2(θ) is a constant of the motion.
(b) derive the other two equations of motion. September 23 2020, 1:39 am
Computational and Applied Mathematics Discussion Group November 12 2018, 8:42 pmsince you used proportionality to calculate force of attraction,I tried to use the general solution f = gmm/r^2 and did convert but the answers are not equal.Where did I go wrong? November 12 2018, 8:42 pm
Computational and Applied Mathematics Discussion Group September 23 2015, 6:49 pmHi guys. I have a question, if someone could explain how to calculate this.
The extinction of the dinousaurs is widely believed to be due to the impact of a very massive meteorite striking the sea, land or both. Consider a smaller meteorite of mass 4 million kg entering the atmosphere vertically at 15 km/s and impacting land in a vertical fashion. You are given that:
1 megaton of TNT is equivalent to 4.2 thousand million million joules
20 kilotons of TNT is the energy associated with the explosion of an atomic bomb
The number of atomic bombs to which the meteorite impact would have been equivalent is approximately.... September 23 2015, 6:49 pm
Computational and Applied Mathematics Discussion Group August 18 2014, 10:19 pmJust as a follow up, correct me if I am wrong, but isn't it that the sun doesn't move? Because when you explain the concept of ecliptic and equinoxes, you talk about the sun as if it is a moving object. August 18 2014, 10:19 pm
Computational and Applied Mathematics Discussion Group August 18 2014, 10:08 pmHi Houston, first of all great videos man, very helpful and you explain in detail, thank you very much for that. Now, the thing that I just want to be sure of is with regards to your drawing of the ecliptic. Does this mean that the equinoxes are at East and West points? Hope I am making sense. August 18 2014, 10:08 pm
Computational and Applied Mathematics Discussion Group August 14 2013, 1:02 amI have created two courses for the Astronomy and the Mechanics sections. This is to enable quick access to content as the two sections are quite different. It would be difficult to look for Astronomy videos in a bunch of Mechanics ones though the course is intended to be a single course as it is done at the University of Witwatersrand in South Africa. The aim is just to reduce the time it will take to get the right videos for the right section.nI have also created a group where you can ask any Astronomy or Mechanics question but asking here achieves the same result. So go ahead and register into the two courses and get the material there if you are doing the courses or just interested. August 14 2013, 1:02 am
Computational and Applied Mathematics Discussion Group August 10 2013, 12:32 pmThis is the discussion group for the Astronomy and Mechanics course where you can ask your questions directly to me and I will answer explaining and concept further that you might have difficulties with. August 10 2013, 12:32 pm
Computational and Applied Mathematics Discussion Group June 15 2013, 11:47 pmWe will be uploading new videos soon for the Applied Mathematics Astronomy courses. Many students find this challenging so during the holidays, feel free to take a look at them and get yourself up to speed. It will definitely be helpful :) June 15 2013, 11:47 pm