Vector nature of mechanics (help)

[jeremy22511]

I suppose I should post it here. It's not really a homework problem...

And my question is: Is the validity of the vector approach in mechanics entirely based on its consistency with experimental results?

Every time I do a question, I use the usual component resolution technique unique to vectors and I can do it correctly. But I can't help but wonder how a practical science can link up so nicely with a subject with only internal coherence like mathematics. And it leads me to think that experimental results are the only basis for the validity of the principles.

Can someone help me with that?? Thanks.

Jeremy

 

[Pengwuino]

Newton created vector calculus in order to describe classical mechanics so it makes sense that mechanics works so well with it.

Although to give you more insight, you could postulate a set of 3 numbers that transform in a certain way that is different from the way vectors transform and you wouldn't be able to do classical mechanics with it. Hell, you could even say let's define position in the 3d space so that given coordinates x,y,z, their position is defined as (e^x, e^y, e^z). Those aren't vectors and if you try to do mechanics with them, it won't work.

 

[kcdodd]

I am wondering how much Newton contributed to the idea vectors. What we consider as vector calculus wasn't developed until the end of the 19th century.