So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie...
Lately, I am trying to find a way to "generalize" my approach classical mechanics. Specifically, I need a system that can always guarantee a solution to any problem. In a sense, just like mathematicians like to generalize stuff. For example, if you get a system of linear equations, you can always solve it by using the Gauss method of substitution...
I often have the problem of seeing why the solution provided by the textbook is right, but I don't see why my solution is wrong... I'm guessing this is the motivation behind my quest.
I know a field as big as mechanics is hard to cover with one or two principles, but I need something to always help me set the correct system up, the rest being "just math". So is there a method that yields a uniform system?
I have heard that Lagrangian mechanics can provide something like this, but I'm not sure whether to take it up... Can anyone post their experiences with that?
Lastly, I would add that I am no stranger to advanced math topics. I like linear algebra and multivariable calculus... from my experience learning new math has always enhanced and deepened my understanding of physics. Don't hesitate if you have to offer something... maybe a book or similar resource...
