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Re: [Phys-l] solving an energy equation





|
| To simplify the problem, imagine throwing a ball straight up
| and it then returns to your hand. I can write down F=ma,
| integrate once to get v(t), and again to get y(t). All clear.
| Alternatively I can re-express dv/dt as dv/dy * v and
| integrate to get v(y). But v isn't a single-valued function
| of y! There are two possible signs for v for a given y! The
| sign information has somehow been lost when I used the chain
| rule. How can I recover it *given* that my goal is to find
| y(t) starting from an equation for (dy/dt)^2?
|
| I'm wondering how I've *ever* managed to solve mechanics
| problems using energy. Clearly I'm somehow inserting the
| correct sign information by hand, perhaps without even
| realizing I'm doing it. If I can do it, there should be a way
| to tell Maple how to do it, shouldn't there?
|

Carl,
When you work the problem by hand, you know doubt work it piece-wise,

A) on the way up
B) on the way down

Your do this as that is how you insert the sign information by hand,

Is there a way to break this up piece-wise in your "Maple" methods.