@ecterrab 

Excellent and thank you! 

(and sorry for the rant!) 

@Kitonum 

Thank you, but this is a serious problem because there are a chain of several steps (too long to check by hand) and in the middle there will be invariably terms like the Q(t)^2*P(t)*Q(t) + Q(t)*P(t)*Q(t)^2 which get handled wrongly and screw up the entire computation.  Do you know what causes the problem (I repeat, it did not exist in Maple 17, which I have on  another computer).

Must be something in the parser, I guess, but I am not sufficiently proficient to open the Physics package and debug. 
The only workaround I could find is a  horrible hack (never simplify anything, then remove the (t) dependence and THEN simplify). 

</rant> As a result I can never be confident that the computation is truly correct, unless I check by hand, which defies the purpose! </rant>