Group Abstract

Message Boards

WOLFRAM COMMUNITY

4.6K Views

5 Replies

1 Total Like

View groups...

Follow this post

Share this post:

GROUPS:

Mathematics Equation Solving Wolfram Language

Determine the equilibrium points of a non-linear system

MANIKANDAN R

Posted 5 years ago

Hi I am trying to determine the equilibrium points in terms of the nondimensional parameters. the following is the non dimensionalised system: Attachments: equation.PNG mate.PNG

POSTED BY: MANIKANDAN R

5 Replies

Sort By:

MANIKANDAN R

Posted 5 years ago

Sir, Herein Mathematica file attached Attachments: my.nb

POSTED BY: MANIKANDAN R

Daniel Lichtblau

Daniel Lichtblau, Wolfram Research

Posted 5 years ago

POSTED BY: Daniel Lichtblau

MANIKANDAN R

Posted 5 years ago

Si thanks, Please find u[x, y, z] := y; v[x, y, z] := (-d* y) - (UMAXJ(tanh[k_ 1sin[x] + k_ 2y + k_ 3z])) + (d_ 2* z) - (sin[x]); w[x, y, z] := (dy) + (UMAXJ(tanh[k_ 1sin[x] + k_ 2y + k_ 3z]) - d_ 2z) + (mu1((UMAXJtanh[k_ 1sin[x] + k_ 2y + k_ 3z]) - d_ 2z)) + (sin[x]); sols = NSolve[{u[x, y, z] == 0, v[x, y, z] == 0, w[x, y, z] == 0}, {u, v, w}, Reals];

Si thanks, Please find

u[x, y, z] := y;

v[x, y, z] := (-d*
     y) - (UMAXJ*(tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z])) + (d_ 2*
     z) - (sin[x]);

w[x, y, z] := (d*y) + (UMAXJ*(tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z]) - 
     d_ 2*z) + (mu1*((UMAXJ*tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z]) - 
       d_ 2*z)) + (sin[x]);

sols = NSolve[{u[x, y, z] == 0, v[x, y, z] == 0, w[x, y, z] == 0}, {u,
     v, w}, Reals];

POSTED BY: MANIKANDAN R

Bill Nelson

Posted 5 years ago

Try u[x_,y_,z_]:= y; v[x_,y_,z_]:= -dy - UMAXJTanh[k1Sin[x] + k2y + k3z] + d2z - Sin[x]; w[x_,y_,z_]:= dy + UMAXJTanh[k1Sin[x] + k2y + k3z] - d2z + Sin[x] + mu1(UMAXJTanh[k1Sin[x] + k2y + k3z] - d2z); Simplify[w[x,y,z]==0,u[x,y,z]==0&&v[x,y,z]==0] which returns mu1*Sin[x]==0

Try

u[x_,y_,z_]:= y;
v[x_,y_,z_]:= -d*y - UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] + d2*z - Sin[x];
w[x_,y_,z_]:=  d*y + UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] - d2*z + Sin[x] +
                mu1*(UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] - d2*z);
Simplify[w[x,y,z]==0,u[x,y,z]==0&&v[x,y,z]==0]

which returns

mu1*Sin[x]==0

POSTED BY: Bill Nelson

MANIKANDAN R

Posted 5 years ago

Thanks

POSTED BY: MANIKANDAN R

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback