I wanted to define system of ode functions for my higher order problems. I have differential equations are :
x=cosy
z=siny
y'=sqrt((lambda*f*p*siny/x)+(siny^2/x^2)-(2/lambda^2)+(2*cosy/lambda)-(3*a*p^2*lambda^2/2))
y"=(-y'*x'/lambda*x)-(cosy/x)-(f*p'/4)-(f*x'*p/4*x)+(y'*cosy/x)+(siny/lambda)+(lambda*f*p*cosy/4*x)+(siny*cosy/x^2)+(mu_1*(sin(y) - mu_2*cos(y)) / (2 * x^2)
where, y,x,p are functions of s. and f,lambda and a are constants.
while defining ode function for my bvp solve, I write the code as
function dydx = odefun2(t, y, params)
lambda = params.lambda;
a = params.a;
f = params.f;
mu_1=params.mu_1;
mu_2=params.mu_2;
y1 = y(1); % y
y2 = y(2); % x
y3 = y(3); % z
y4 = y(4); % p
y5 = y(5); % p_dot
y6 = cos(y1); %x_dot
y7 = sin(y1); %z_dot
ydot = sqrt((lambda * f * y4 * sin(y1) / y2) + (sin(y1)^2 / y2^2) - (2 / lambda^2) + (2 * cos(y1) / lambda) - (3 * a * (y4^2) * lambda^2)/2);
yddot = -((ydot * cos(y1) / (lambda * y2))) - (cos(y1) / y2) - (0.5 * y5 / 4) - (0.5 *cos(y1) * y4 / (4 * y2)) + (ydot * cos(y1) / y2) + (sin(y1) / lambda) + (0.5 * lambda * y4 * cos(y1) / (4 * y2)) + (sin(y1) * cos(y1) / y2^2) + (mu_1*(sin(y1) - mu_2*cos(y1)) / (2 * y2));
dydx = [y5; y6; y7; ydot; yddot];
end
But I have no equation for p'. And I am not sure that how can I relate x and z with x' and z' respectively. Also I don't have any differential equation for p'. how I should relate p and p'?
need some suggestions.
