I have got a problem in assigning a variable as constant and solving a equations for minimum value. These are my equations:
kd (2 h2 Cos[[Theta]2] - b2 Sin[[Theta]2]) (b1 - (b1 + b2) Cos[[Theta]1] + b2 Cos[[Theta]2] + 2 h1 Sin[[Theta]1] + 2 h2 Sin[[Theta]2]) == (b2 g (m2 + md) + h2 (m2 + 2 md) xg) Cos[[Theta]2] + (g h2 (m2 + 2 md) - b2 (m2 + md) xg) Sin[[Theta]2]
Sin[[Theta]1] (b1^2 kd + b1 b2 kd - g h1 (m1 + 2 (m2 + md)) - b2 (m2 + md) xg - b1 (m1 + m2 + md) xg + (b1 + b2) kd (b2 Cos[[Theta]2] + 2 h2 Sin[[Theta]2])) + Cos[[Theta]1] (b2 g (m2 + md) + b1 (2 h1 kd + g (m1 + m2 + md)) - h1 (m1 + 2 (m2 + md)) xg + 2 h1 kd (b2 Cos[[Theta]2] + 2 h2 Sin[[Theta]2])) == 2 (b1 + b2) h1 kd Cos[2 [Theta]1] + 1/2 ((b1 + b2)^2 - 4 h1^2) kd Sin[2 [Theta]1]
[Theta]20 > [Theta]10
[Theta]10 > 0
By using these four equation how can I found minimum value of xg. In this problem there are only three variable rest of all other are constant. The three variables are [Theta]10, [Theta]20 and xg. I tried to use Reduce{} command but I don't know which is suitable for this problem. Please be kind enough to assist in this regard. Thank you in advance for responding.