The problem is
Using the equations of motion for the simple pendulum in cartesian coordinates (Eq.(3.7)), numarically integrate the trajectory for the initial conditions
(θ, θ') = (0.1, 0)
Plot the pendulum angle
theta[t] and the pendulum length
l[t]=sqrt[x[t]^2+y[t]^2] as a function of time.
The equation (3.7) is
x''[t] == (-x[t] x'[t]^2 - x[t] y'[t]^2 + x[t] y[t] g)/l[t]^2 y''[t] == (-y[t] x'[t]^2 - y[t] y'[t]^2 - x[t]^2 g)/l[t]^2
At first i try to make EOM(equation of motion) only express for
y[t]. So use
l[t]=sqrt[x[t]^2+y[t]^2]]. And in this problem the initial boundary condition expressed polar coordinate, sine I try to change IBC(Initial Boundary Condition) as
θ[t] == ArcTan[y[t]/x[t]]; Tan[θ[t]] == Sin[θ[t]]/Cos[θ[t]] == y[t]/x[t]
Actually I don't know that another two IBC correctly.
there is my process by using Mathematica and solutions what I want to plot. Actually I just try to make to plot similarly to solution. So I was assumed the one of IBC.
That is, I want to know method of changing IBC, and I want to plot the graph in solution.