@Preben Alsholm, I change several parts of these expressions as constants and I got solution, but I really don't understand why I can't get this solution for full system of six equations.

Simple.mw

@Preben Alsholm, you are wrong. I have 8 equations, but I can choose six of them for calculation of 6 variables. At the same time I guess that the remaining two variables are constants.

@Kitonum, unfortunately, it didn't help. The result is the same.

Quasi-static2.mw

@acer, You are right, for me, visually good expression is better, it is E2 (variant of @Kitonum), but I understand that from program view E1 is shorter. Nevertheless, many thanks for the answers, it helps a lot!

@acer, thank you, it works good. But I have misunderstanding, in following example I have not full simplification again:
 

Download trigon.mw

In this example Maple combined part of expression and forgot about this: 

-2*diff(x(t), t)*sin(psi(t))*cos(theta__si(t))*diff(theta__si(t), t)*`l__1с` + diff(z(t), t)^2 - 2*cos(psi(t))*cos(theta__si(t))*diff(theta__si(t), t)*diff(z(t), t)*`l__1с`

I understood, that we can manually optimize our expression, but it's not effective by using freeze for some expression parts. Is it possible to carry out it automatically by set of some commands?

@acer, thank you so much for the full answers. Problem with symbol "c" was due to of Russian language and program for automatically switching keyboard layouts. I apologize for the concern, but there is one more question. How can I simplify my expression more effectively? For example:
 

Download PotenEnergy.mw In this expression we can take out the multipliers (m1+m2+mf) and g, also we can replace sin(180-fi) as sin(fi). I try to use factor, but it works like expand.

@Kitonum, I am very grateful to you! Could you comment why previous representation didn't work? Just for my better understanding of Maple logic.

P.S. Simplification wasn't applied, "simplify" just substitutes the expressions.  I used this:

V__2si := t -> simplify((V__2six^2 + V__2siy^2 + V__2siz^2)(t), trig)

, but it's not effective.

I plan to calculate the Lagrange equations in Maple. These equations contain many variables and require working with trigonometric expressions and differentiation. I tried to implement the approach you described, but did not get the result. I attached a file, could you tell me what I'm wrong about?

equations.mw

@tomleslie, is the "trig" in combine function a simplification procedure? Can I use several types of expression simplification?

@acer, Thank you very much for the answer with explanations!