I have been running code to solve the following equations for hours and hours, but there are still no solutions! I am new to Mathematica, so I am not really sure whether or not it is a good idea to use Reduce
to solve trigonometric equations.
Also, I want a symbolic solution, NOT a numeric one.
The code is:
eq1 := (Sin[
Subscript[θ, 1] - Subscript[θ,
3]] (-Sin[
Subscript[θ, 2] - Subscript[θ, 7]] Subscript[
a, 1] + Cos[
Subscript[θ, 2] - Subscript[θ, 7]] Subscript[
a, 2]) +
Sin[Subscript[θ, 1] - Subscript[θ,
2]] (Sin[
Subscript[θ, 3] - Subscript[θ, 7]] Subscript[
b, 1] + Cos[Subscript[θ,
7]] (-Cos[Subscript[θ, 3]] +
Sin[Subscript[θ, 3]]) Subscript[b, 2])) Subscript[l,
1] Subscript[l, 2] Subscript[l, 3];
eq2 := Sin[
Subscript[θ, 1] - Subscript[θ,
4]] (-Cos[
Subscript[θ, 2] - Subscript[θ, 7]] Subscript[a,
2] + Sin[
Subscript[θ, 2] - Subscript[θ, 7]] (Subscript[a,
1] - Subscript[b, 1]) +
Cos[Subscript[θ,
7]] (Cos[Subscript[θ, 2]] -
Sin[Subscript[θ, 2]]) Subscript[b, 2]) Subscript[l, 1]
Subscript[l, 2] Subscript[l, 4];
eq3 := 1/2 Cos[Subscript[θ, 1]] Sin[
Subscript[θ, 2] - Subscript[θ,
5]] (-2 Sin[
Subscript[θ, 3] - Subscript[θ, 7]] Subscript[b,
1] + 2 Cos[Subscript[θ,
7]] (Cos[Subscript[θ, 3]] -
Sin[Subscript[θ, 3]]) Subscript[b, 2]) Subscript[l, 1]
Subscript[l, 2] Subscript[l, 3] Subscript[l, 5];
eq4 := -Sin[
Subscript[θ, 1] - Subscript[θ,
4]] (-Cos[Subscript[θ, 6]] Sin[
Subscript[θ, 2] - Subscript[θ, 7]] Subscript[a,
1] + Cos[Subscript[θ, 6]] Cos[
Subscript[θ, 2] - Subscript[θ, 7]] Subscript[a,
2] + Cos[Subscript[θ,
2]] (Sin[
Subscript[θ, 6] - Subscript[θ, 7]] Subscript[
b, 1] + Cos[Subscript[θ,
7]] (-Cos[Subscript[θ, 6]] +
Sin[Subscript[θ, 6]]) Subscript[b, 2])) Subscript[l,
1] Subscript[l, 2] Subscript[l, 4] Subscript[l, 6];
eq5 := -Sin[Subscript[θ, 2] - Subscript[θ, 3]] Sin[
Subscript[θ, 1] - Subscript[θ, 4]] Subscript[l, 1]
Subscript[l, 2] Subscript[l, 3] Subscript[l, 4];
eq6 := Sin[Subscript[θ, 1] - Subscript[θ, 3]] Sin[
Subscript[θ, 2] - Subscript[θ, 5]] Subscript[l, 1]
Subscript[l, 2] Subscript[l, 3] Subscript[l, 5];
eq7 := -Sin[Subscript[θ, 1] - Subscript[θ, 2]] Sin[
Subscript[θ, 3] - Subscript[θ, 6]] Subscript[l, 1]
Subscript[l, 2] Subscript[l, 3] Subscript[l, 6];
sols := Reduce[{eq1 == 0, eq2 == 0, eq3 == 0, eq4 == 0, eq5 == 0,
eq6 == 0, eq7 == 0}, {Subscript[θ, 1], Subscript[θ,
2], Subscript[θ, 3], Subscript[θ, 4],
Subscript[θ, 5], Subscript[θ, 6],
Subscript[θ, 7]}];
Any help will be appreciated.
NSlove
cannot solve these 7 eqs either! Anyway, I do enhance my next codes :-) $\endgroup$