Could someone help me with a mathematical formula for N connected pendulums? Some simplified approach, because I know that for 3 pendulums the formula is huge.
Using a Lagrangian formulation:
Euler-Lagrange equation for each angle:
Various initial derivatives:
LHS:
RHS:
Equating (and cancelling an l
):
So we arrive at a classic Ax = b
type matrix equation that needs to be solved. This does indeed become very unwieldy even at low values of N
, so a numerical solution is preferable (e.g. LU decomp.)
Test for N = 2
:
Solving these (simply multiply a^-1
with b
and rearrange) gives the results on this page and this page, both of which seem to contradict the link you gave.