Hello. I'm not exactly sure about your question, but AFAIK Matlab uses the Maple V symbolic algebra engine. It's not always possible to simplify expressions either because they don't simplify or it can't figure out how you want to simplify them. I think the simplify command has various options, like trig, that can be used to guide the simplification, e.g. to search for terms that are polynomial in trigonometric functions. Another way might be to substitute the terms you want to simplify in by other variables e.g. a=sin(theta), b=cos(theta), and try to simplify that. Maybe you could post the differential equation you are working with?

There are several repeating expressions. You just need to spot them on by yourself.

I think it is better to use Mathematica, that is very easy to calculate controlled Lagrange.

what about using simulink simmechanics .... this tool can make many bodies and joints and give the physical model instead of the mathematical model

 Thanks all,

I want to comment on your answers, but we don't have option for comments - ( I think researchgate should developed such functionality)' - , either one need to follow the searcher and send him a private message which may take time, and also s not public because audience might need to see the discussion; or you put like an answer, which the way I don't like to use, any way:

As for Graham W Pulford, my code is too long, and I don't want disturb the others, I send him private message.

I don't know what Barkan Ugurlu mean, I'm talking about a couple of pages per a single term !!!!!

Regarding, Jose Victor Nunez Nalda , I didn't understand, what did he meant by 'result was the same', Did he mean result was same as mine (very long) or, the result by hand and code was same ,,,

For, Mohamed Dinary, I agree with simmechanics is useful, but you know I have to mathematical model , then if time allowed I may go for that; moreover, I'm not experienced in SimMechanics, I just used to work on simple system, (inverted pendulum), and didn't get attracting results, could you please suggest to me some resources to learn more about SimMechaincs,

The good news is that, I got another approach that can help to derive the dynamic model, based on the parametrization of the manipulator via twists, described by Murray, A Mathematical Introduction to Robotic Manipulation, I can give some details later if you like. sorry for being long,,,

Thanks.