Need help solving an differential equation problem

Hi !

I am a begginer in matlab and i am having some problems solving and ploting a system of differential equations with initial condition. The equation is defined as

r''(t) = Ft * r(t) + (0,0,m*g)

Ft = (1- llr(t)ll ) / llr(t)ll

where r(t) = (x(t), y(t), z(t)), llr(t)ll is lenght of vector r at time t and r(0) = (sin(45), 0, sin(45)), r'(0) = (0, 2, 0).

My code:

m=2;

g=9.8;

h=300;

syms x(t) y(t) z(t)

Ft = ((1/(x(t)^2+y(t)^2+z(t)^2)^(1/2))-1)*h;

eqns = [diff(x,t,2)== Ft*x, diff(y,t,2)==Ft*y, diff(z,t,2)==Ft*z+m*g];

cond = [y(0)==0, diff(y,0)==3, diff(x,0)==0, diff(z,0)==0, x(0)==(1/2)^(1/2), z(0)==(1/2)^(1/2)];

S = dsolve(eqns, cond);

fplot3(x(t),y(t),z(t))

Command window:

>> poskusi

Warning: Number of equations greater than number of indeterminates. Trying heuristics to reduce to square system.

> In symengine

In mupadengine/evalin_internal

In mupadengine/feval_internal

In dsolve>mupadDsolve (line 334)

In dsolve (line 203)

In poskusi (line 9)

Error using mupadengine/feval_internal

Unable to reduce to square system because the number of equations differs from the number of indeterminates.

Error in dsolve>mupadDsolve (line 334)

T = feval_internal(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 203)

sol = mupadDsolve(args, options);

Error in poskusi (line 9)

S = dsolve(eqns, cond);

Any suggestions for fixing it?

Thank you!

Answer 1

[Shiva Kalyan Diwakaruni]

Hi,

'Unable to reduce to square system because the number of equations differs from the number of indeterminates.'

This error is indicating the this problem is unsolvable with the given information. To solve the system of differential equations with all these conditions, you need to include more information on one of the variables. One of the variables is missing either a differential equation, a function or actual values. One of these is required in order to solve these equations for the desired constants.

Hope it helps.