It is a rigid pendulum at the end of which another rigid pendulum is attached. The two inextensible rods of lengths and
have zero mass. The 2 masses at the ends are of masses
and
, which will be considered as punctual. The double pendulum is therefore fixed in O and articulated freely in
. The movement takes place in a plane of horizontal
and vertical
coordinates. We will consider that the two stems can “cross” without problem. The angle that the pendulum 1 makes with the vertical is denoted
and the angle that the pendulum 2 makes with the vertical is denoted
. These angles are noted positively counterclockwise.
By setting , we obtain the following system:
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations.
The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
We're using this method here.
The output gif is :
