"much greater than (>>) " operator calculation

I have calculated C1, C2 and B1. And than I need to simplify the three equations with the condition of K1>> lamba1 (K1 much greater than lamba1) but because of the the equation results are very complication. Therefore, I would like to try find if it is possible to use matlab to simplify the the condition of K1>> lamba1(K1 much greater than lamba1).

Below is my code.

If there is any suggestion please feel free to let me know!

Thank you very much!

clc
clear
format long
syms q h v E G S D I a q_o phi_o
syms x y k1 C1 B1 C2 lamda1 lamda1_bar k1 k1_bar
phi=phi_o*cos(lamda1*x)*cos(lamda1*y)+((C1*cosh(lamda1*y)+C2*y*sinh(lamda1*y))*cos(lamda1*x)...
    +(C1*cosh(lamda1*x)+C2*x*sinh(lamda1*x))*sin(lamda1*y));

psi=B1*(sinh(k1*y)*sin(lamda1*x)-sinh(k1*x)*sin(lamda1*y));
deta_phi=diff(phi,x,2)+diff(phi,y,2);

% Eq7.93
W=phi-(D/S)*deta_phi;
Eq_793=subs(W,x,a/2);
Eq_793=subs(Eq_793,(a*lamda1)/2,lamda1_bar);
Eq_793=simplify(Eq_793)

Eq_793 = 

% Eq7.94
Eq_794=diff(phi,x,2)+v*diff(phi,y,2)-(1-v)*diff((diff(psi,x,1)),y,1);
Eq_794=subs(Eq_794,x,a/2);
Eq_794=subs(Eq_794,(a*lamda1)/2,lamda1_bar);
Eq_794=subs(Eq_794,(a*k1)/2,k1_bar);
Eq_794=simplify(Eq_794)

Eq_794 = 

% Eq7.95
Eq_795=2*diff(diff(phi,x,1),y,1)+diff(psi,x,2)-diff(psi,y,2);
Eq_795=subs(Eq_795,x,a/2);
Eq_795=subs(Eq_795,(a*lamda1)/2,lamda1_bar);
Eq_795=subs(Eq_795,(a*k1)/2,k1_bar);
Eq_795=simplify(Eq_795)

Eq_795 = 

eqns=[Eq_793==0,Eq_794==0,Eq_795==0];
S=solve(eqns,C1,C2,B1)

S = struct with fields:
    C1: -(- 8*D*k1*lamda1^3*phi_o*cosh(k1*y)*cos(lamda1*y)^2*cos(lamda1_bar)^2*sinh(lamda1_bar) + 4*D*lamda1^4*phi_o*cos(lamda1*y)*sin(lamda1*y)^2*cos(lamda1_bar)*cosh(lamda1_bar)*sinh(k1_bar) + 4*S*k1^2*phi_o*cos(lamda1*y)*sin(lamda1*y)^2*cos(lamda1_…
    C2: (4*(- 2*D*k1*lamda1^4*phi_o*cosh(k1*y)*cos(lamda1*y)^2*cos(lamda1_bar)^2*sinh(lamda1_bar) - S*k1*lamda1^2*phi_o*cosh(k1*y)*cos(lamda1*y)^2*cos(lamda1_bar)^2*sinh(lamda1_bar) + D*lamda1^5*phi_o*cos(lamda1*y)*sin(lamda1*y)^2*cos(lamda1_bar)*cosh…
    B1: (2*(4*D*lamda1^4*phi_o*sin(lamda1*y)^3*cosh(lamda1_bar)^2*sin(lamda1_bar) + 4*S*lamda1^2*phi_o*sin(lamda1*y)^3*cosh(lamda1_bar)^2*sin(lamda1_bar) - 4*D*lamda1^4*phi_o*v*sin(lamda1*y)^3*cosh(lamda1_bar)^2*sin(lamda1_bar) - 4*D*lamda1^4*phi_o*co…

C1 = vpa(S.C1, 5)

C1 = 

C2 = vpa(S.C2, 5)

C2 = 

B1 = vpa(S.B1, 5)

B1 = 

Answer 1

[Shreeya]

Hi Mark

I understand that you want to implement the much greater than (>>) operator to solve the equation K >> lambda in MATLAB.

You can define a tolerance level , let’s say of value 100. If this tolerance level is satisfied, it can be concluded that K >> lambda. The MATLAB function “assume” can help enforce this assumption while solving equations.

assume(T > 100)

The above code enforces the much greater than constraints to solve the equations further.

Refer to the documentation for more details: Set assumption on symbolic object - MATLAB assume - MathWorks India

Hope this helps!