Understanding Energy Methods in Classical Mechanics

AI Thread Summary
Energy methods in classical mechanics simplify problem-solving by focusing on the conservation of total energy rather than calculating forces and accelerations directly. For instance, analyzing a frictionless roller coaster track illustrates how energy methods streamline calculations compared to Newtonian approaches, which require tedious force assessments. While methods like virtual work, Lagrange equations, and Hamilton equations are effective, they also have limitations that practitioners should be aware of. Resources such as specific academic websites can provide further insights into these methods. Understanding energy methods enhances problem-solving efficiency in mechanics.
chandran
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While solving classical mechanics problems there is a wide feeling that

energy methods can be used to solve any problem.

What is energy method. How is it different from other methods?
Any example please.
 
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Read any chapter in your book on energy, that should answer your questions.
 
Here's a problem that is more easily solved with an energy method: the roller coaster.
For simplicity, consider a point particle on a frictionless roller coaster track. With Newtonian methods, you need to know the net force on the particle to determine its acceleration (and its initial conditions to determine the motion). However, the net force varies along the track since the free-body diagram varies. By hand, this approach is tedious to calculate the whole motion. One could use a computer to carry out the calculation. An energy method using the "Conservation of Total Energy" makes the problem much simpler.

Examples of energy methods: virtual work, Lagrange Eqs, Hamilton Eqs, etc.
However, these energy methods have limitations as well.
 
any web on this?
 
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