Help me understand!
11 vues (au cours des 30 derniers jours)
I am presented with a task of simulating the movement of three bodies with a constant mass using Newton's laws.
The task is very easy to follow and I have no trouble understanding it, until it comes to solving the differential equation using Runge-Kutta, where M is the mass of a body, is the second derivative of the position, namely, the acceleration and F is the force applied on M due to the two other masses.
Please refer to task number 3 below
Where equation 3 is I am finding it particularly difficult to understand why the right hand of the equation is a column consisten of what appears to be the velocity V for each body and the acceleration .
I would highly appreciate any guidance to the interpertation of the task!
AndresVar le 14 Fév 2022
Modifié(e) : AndresVar le 16 Fév 2022
Equation 3 is a 2nd order system p''=..., the RK3 is given for 1st order p'=...(see it's first difference ) =..)
See for example equation 14 here: part1.pdf (nyu.edu)
you can see how order is reduced by introducing firts time derivatives (V's) as new variables