#SOLUTIONS A,B,E AND T IN SPHERICAL POLAR COORDINATES
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uR:=simplify((diff(phi(R,theta,beta),R)
+R*cos(beta)*diff(omega(R,theta,beta),R)
-(3-4*nu)*cos(beta)*omega(R,theta,beta)
+(2/R)*diff(psi(R,theta,beta),theta)
+R*cos(beta)*diff(chi(R,theta,beta),R)
+chi(R,theta,beta)*cos(beta))/(2*mu));
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ut:=simplify(((1/R*sin(beta))*diff(phi(R,theta,beta),theta)
+cot(beta)*diff(omega(R,theta,beta),theta)
-2*sin(beta)*diff(psi(R,theta,beta),R)
-2*(cos(beta)/R)*diff(psi(R,theta,beta),beta)
+cot(beta)*diff(chi(R,theta,beta),theta))/(2*mu));
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ub:=simplify((1/R)*(diff(phi(R,theta,beta),beta)
+cos(beta)*diff(omega(R,theta,beta),beta)
+(3-4*nu)*sin(beta)*omega(R,theta,beta)
+2*(cot(beta)/R)*diff(psi(R,theta,beta),theta)
+cos(beta)*diff(chi(R,theta,beta),beta)
-chi(R,theta,beta)*sin(beta))/(2*mu));
#
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sRR:=simplify(diff(phi(R,theta,beta),R,R)
+R*cos(beta)*diff(omega(R,theta,beta),R,R)
-2*(1-nu)*cos(beta)*diff(omega(R,theta,beta),R)
+(2*nu/R)*sin(beta)*diff(omega(R,theta,beta),beta)
+(2/R)*diff(psi(R,theta,beta),R,theta)
-(2/R^2)*diff(psi(R,theta,beta),theta)
+R*cos(beta)*diff(chi(R,theta,beta),R,R)
+(2*sin(beta)/R)*diff(chi(R,theta,beta),beta));
#
stt:=simplify((1/R)*diff(phi(R,theta,beta),R)
+(cot(beta)/R^2)*diff(phi(R,theta,beta),beta)
+(1/(R*sin(beta))^2)*diff(phi(R,theta,beta),theta,theta)
+(1-2*nu)*cos(beta)*diff(omega(R,theta,beta),R)
+(2*nu/R)*sin(beta)*diff(omega(R,theta,beta),beta)
+(cos(beta)^2/(R*sin(beta)))*diff(omega(R,theta,beta),beta)
+(cot(beta)/(R*sin(beta)))*diff(omega(R,theta,beta),theta,theta)
+(2/(R*sin(beta))^2)*diff(psi(R,theta,beta),theta)
-(2/R)*diff(psi(R,theta,beta),R,theta)
-(2*cot(beta)/R^2)*diff(psi(R,theta,beta),beta,theta)
+(cot(beta)/(R*sin(beta)))*diff(chi(R,theta,beta),theta,theta)
-cos(beta)*diff(chi(R,theta,beta),R)
+((1+sin(beta)^2)/(R*sin(beta)))*diff(chi(R,theta,beta),beta));
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sbb:=simplify((1/R)*diff(phi(R,theta,beta),R)
+(1/R^2)*diff(phi(R,theta,beta),beta,beta)
+(cos(beta)/R)*diff(omega(R,theta,beta),beta,beta)
+(1-2*nu)*cos(beta)*diff(omega(R,theta,beta),R)
+(2*(1-nu)*sin(beta)/R)*diff(omega(R,theta,beta),beta)
+(2*cot(beta)/R^2)*diff(psi(R,theta,beta),theta,beta)
-2*(cot(beta)/R)^2*diff(psi(R,theta,beta),theta)
+(cos(beta)/R)*diff(chi(R,theta,beta),beta,beta)
-cos(beta)*diff(chi(R,theta,beta),R));
#
stb:=simplify((1/(R^2*sin(beta)))*diff(phi(R,theta,beta),theta,beta)
-(cot(beta)/(R^2*sin(beta)))*diff(phi(R,theta,beta),theta)
+(cot(beta)/R)*diff(omega(R,theta,beta),beta,theta)
+(2*(1-nu)/R)*diff(omega(R,theta,beta),theta)
-(1/(R*sin(beta)^2))*diff(omega(R,theta,beta),theta)
+(cot(beta)/(R^2*sin(beta)))*diff(psi(R,theta,beta),theta,theta)
-(sin(beta)/R)*diff(psi(R,theta,beta),R,beta)
-(cos(beta)/R^2)*diff(psi(R,theta,beta),beta,beta)
+(1/(R^2*sin(beta)))*diff(psi(R,theta,beta),beta)
+(cot(beta)/R)*diff(chi(R,theta,beta),theta,beta)
-(1/(R*sin(beta)^2))*diff(chi(R,theta,beta),theta));
#
sbR:=simplify((1/R)*diff(phi(R,theta,beta),beta,R)
-(1/R^2)*diff(phi(R,theta,beta),beta)
+(1-2*nu)*sin(beta)*diff(omega(R,theta,beta),R)
+cos(beta)*diff(omega(R,theta,beta),beta,R)
-(2*(1-nu)*cos(beta)/R)*diff(omega(R,theta,beta),beta)
+(1/R^2)*diff(psi(R,theta,beta),theta,beta)
+(cot(beta)/R)*diff(psi(R,theta,beta),theta,R)
-(2*cot(beta)/R^2)*diff(psi(R,theta,beta),theta)
+cos(beta)*diff(chi(R,theta,beta),R,beta)
-sin(beta)*diff(chi(R,theta,beta),R));
#
sRt:=simplify((1/(R*sin(beta)))*diff(phi(R,theta,beta),R,theta)
-(1/(R^2*sin(beta)))*diff(phi(R,theta,beta),theta)
+cot(beta)*diff(omega(R,theta,beta),R,theta)
-(2*(1-nu)*cot(beta)/R)*diff(omega(R,theta,beta),theta)
+(1/(R^2*sin(beta)))*diff(psi(R,theta,beta),theta,theta)
-sin(beta)*diff(psi(R,theta,beta),R,R)
-(cos(beta)/R)*diff(psi(R,theta,beta),R,beta)
+(2*cos(beta)/R^2)*diff(psi(R,theta,beta),beta)
+(sin(beta)/R)*diff(psi(R,theta,beta),R)
+cot(beta)*diff(chi(R,theta,beta),R,theta));
#
T:=simplify(((1-nu)/(mu*alpha*(1+nu)))*
(cos(beta)*diff(chi(R,theta,beta),R)
-(sin(beta)/R)*diff(chi(R,theta,beta),beta)));
qR:=simplify(((1-nu)*K/(mu*alpha*(1+nu)))*
((sin(beta)/R)*diff(chi(R,theta,beta),R,beta)
-cos(beta)*diff(chi(R,theta,beta),R,R)
-(sin(beta)/R^2)*diff(chi(R,theta,beta),beta)));
qt:=simplify(((1-nu)*K/(mu*alpha*(1+nu)))*
((1/R^2)*diff(chi(R,theta,beta),beta,theta)
-(cot(beta)/R)*diff(chi(R,theta,beta),R,theta)));
qb:=simplify(((1-nu)*K/(mu*alpha*(1+nu)))*
((sin(beta)/R)*diff(chi(R,theta,beta),R)
-(cos(beta)/R)*diff(chi(R,theta,beta),R,beta)
+(sin(beta)/R^2)*diff(chi(R,theta,beta),beta,beta)
+(cos(beta)/R^2)*diff(chi(R,theta,beta),beta)));