rigid body dynamics?
Unfortunately, the answer is a big YES. Solving dynamics problems in the real world is very very rarely done by hand. In fact, solving any real-world problem is rarely done by hand these days. An experienced engineer might visualize the problem at hand and simplify the system to a certain point such that he could come up with a quick approximation of the entire system, but to solve the real system, one usually needs computer help.
In the old days, hundreds of engineers were involved in solving one system (by hand) because computer power was so limited at the time. It still had to be done, though. But today, one should put more time in understanding the physics than doing raw number crunching, wouldn't you agree? It is our opinion that it is not OK to use computers to help you understand a problem, but once the physics is understood, leave the computation to the machines. They do a better job there.