1
$\begingroup$

Here's an equations from mechanics:

eq1 := Xa2 + Xb2 - (m1 + m2)*g*Sin[φ] + Fc == 0
eq2 := Ya2 + Yb2 - (m1 + m2)*g*Cos[φ] - Fe - F1 + Fr*Sin[α] == 0
eq3 := Za2 + Fr*Cos[α] == 0
eq4 := Yb2*2*R - F1*R - Fe*(R - x*Cos[α]) + Fr*R*Sin[α] - (R*m1 + m2*(Rx*Cos[α]))*g*Cos[φ] == 0
eq5 := -Xb2*2*R - Fc*(R - x*Cos[α]) - (R*m1 + m2*(R - x*Cos[α]))*g*Sin[φ] == 0
eq6 := Mvr - Fc*x*Sin[α] - g*Sin[φ]*(4*R/(3*π)*m1 + m2*x*Sin[α]) == 0
Solve[{eq1, eq2, eq3, eq4, eq5, eq6}, {Xa2, Xb2, Ya2, Yb2, Za2}]

Answer from book is

$\endgroup$
0

1 Answer 1

2
$\begingroup$
Clear["Global`*"]

eq1 := Xa2 + Xb2 - (m1 + m2)*g*Sin[φ] + Fc == 0;
eq2 := Ya2 + Yb2 - (m1 + m2)*g*Cos[φ] - Fe - F1 + 
    Fr*Sin[α] == 0;
eq3 := Za2 + Fr*Cos[α] == 0;
eq4 := Yb2*2*R - F1*R - Fe*(R*x*Cos[α]) +
    Fr*R*Sin[α] - (R*m1 + m2*(Rx*Cos[α]))*g*Cos[φ] == 
   0;
eq5 := -Xb2*2*R - Fc*(R - x*Cos[α]) -
    (R*m1 + m2*(R - x*Cos[α]))*g*Sin[φ] == 0;
eq6 := Mvr - Fc*x*Sin[α] -
    g*Sin[φ]*(4*R/(3*π)*m1 + m2*x*Sin[α]) == 0;

Solve[{eq1, eq2, eq3, eq4, eq5, eq6}, {Xa2, Xb2, Ya2, Yb2, Za2}]

(* {} *)

The system is overdetermined. Looking at the Options for Solve

Options[Solve]

(* {Cubics -> Automatic, GeneratedParameters -> C, InverseFunctions -> Automatic,
  MaxExtraConditions -> 0, Method -> Automatic, Modulus -> 0, 
 Quartics -> Automatic, VerifySolutions -> Automatic, 
 WorkingPrecision -> ∞} *)

Then specifically at the option MaxExtraConditions

?MaxExtraConditions

enter image description here

(sol = Solve[{eq1, eq2, eq3, eq4, eq5, eq6}, {Xa2, Xb2, Ya2, Yb2, Za2}, 
     MaxExtraConditions -> 1][[1]]) // Column

enter image description here

Each ConditionalExpression has the same condition

assume = sol[[All, -1, -1]] // Union

(* {-3 Mvr π + 3 Fc π x Sin[α] + 4 g m1 R Sin[φ] + 
   3 g m2 π x Sin[α] Sin[φ] == 0} *)

To eliminate the condition, you can either Simplify using this assumption or use Normal

(soln = sol // Normal) // Column

enter image description here

To solve for Xa2 and Ya2 in terms of Xb2 and Yb2

(soln2 = Solve[soln[[1 ;; 4]] /. Rule :> Equal, {Xa2, Ya2}, {R, x}][[1]] // 
    Simplify) // Column

enter image description here

$\endgroup$
1
  • $\begingroup$ After changing the third equation to eq3 := Za2 - Fr*Cos[α] == 0 and executing all of the code, I do not get an error message. What error message are you getting? $\endgroup$
    – Bob Hanlon
    Commented Aug 25, 2019 at 16:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.