# Can Newton's Equation of Motion be Integrated Analytically for Certain Chemical Systems?

In molecular dynamics, one typically integrates Newton's equation of motion, for example using a leap-frog algorithm. Are there chemical systems, for which an analytic integration is a viable alternative? Are there even simulation programs doing this?

• I am not sure about the existence of chemical systems that would need analytic integration, but when you ask if there are simulation programs doing analytical integration, do you mean performing integration using symbols through a computer algebra system? Because other than this, any "program" performing integration is doing numerical integration. – Mythreyi May 13 at 13:30
• @Mythreyi: I was thinking of having the benefits (accurracy, speed of reevaluation, ...) for a chemical system rather then an actual "need", since I suppose the analytic solution is traditionally more difficult and therefore no system "needs" it. And for your question, "doing analytical integration, do you mean performing integration using symbols through a computer algebra system?": yes, exactly, just like e.g. Mathematica does it. – BernhardWebstudio May 13 at 18:21