using solve, 4eqs 4unkns

I'm trying to understand why the output of the following is giving me a 4x1 matrix for the desired solutions. There should only be one discrete value for a1, a2, p1, p2.

t=0;

syms a1 a2 p1 p2

x1=(-1/3)+a1*(1/3)*sin(sqrt(2)*t+p1)-a2*(1/3)*sin(2*t+p2);

x2=-1+a1*sin(sqrt(2)*t+p1)+a2*sin(2*t+p2);

v1=a1*(1/3)*sqrt(2)*cos(sqrt(2)*t+p1)-a2*(1/3)*2*cos(2*t+p2);

v2=a1*sqrt(2)*cos(sqrt(2)*t+p1)+a2*2*cos(2*t+p2);

soln=solve(x1,x2,v1,v2);

soln.a1

soln.a2

soln.p1

soln.p2

I have found the solutions by other means which are a1=1, a2=0, p1=pi/2, p2=pi/2. The answers matlab is returning is:

ans =

-1

1

-1

1

ans =

0

0

0

0

ans =

-pi/2

pi/2

-pi/2

pi/2

ans =

pi

pi

0

0

Any help would be appreciated.

TY

Answer 1

[Alan Stevens]

There are, in fact, an infinite number of possible solutions. When t = 0 the equations can be written and manipulated as follows:

Matlab clearly just provides four simple possibilities!