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Generalized coordinates,

by Trenthan
Tags: coordinates, generalized
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Trenthan
#1
Apr19-09, 03:34 AM
P: 56
1. The problem statement, all variables and given/known data

We two beams of timber, of identical length joined together at the middle, perpendicular forming a "X" in a sense. Underneath the end of each beam we have a spring attached, thus 4 in total. 3 have identical spring constants and the forth is greater than the other 3. We are told each springs natural length, and to assume the COM is at the join between the beams

I need to model this using lagrangian mechanics. Now where i am stuck is picking the generalized coordinates. Checking the answer it says there are 3 but im un-sure as to what they are

2. Relevant equations

NOT really relevant
"lagrangian" L = T(kinetic energy) - V(potential energy).


3. The attempt at a solution

Thinking in cartesion intially i thought sphereical corrdinates, thus (theta, thi, and r). This would allow me to find the spring height wether in compression or extension. This didnt really help me form a "lagrangian" L = T(kinetic energy) - V(potential energy).

So i think i made a mistake after some reading and the generalized coordinates should be related to describing the Centre of mass of the system similar to post by "phagist", titled "Generalized coordinates of a couple harmonic oscillator" looks very similar.

1. So in my case would i still need 2 angles to describe tilt between x-z, y-z, and one for the centre of mass height or is this the height of each individual spring?
2. I thought generalized coordinates can only describe a distance??? how can a angle a generalied coordinate???,

Thanks in advance TRENT
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