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Q & A: Why Hamiltonian formalism is easier to handle?

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Most recent answer: 05/21/2015
Q:
Why Hamiltonian formalism is easier to handle than Lagrangian formalism?
- AYAN (age 22)
INDIA
A:

All three formalisms (Newton, Lagrange and Hamilton) that are employed in classical mechanics are fundamentally equivalent to each other, so what you get from them is in principle the same. In the hamiltonian formalism, you would have 2 coupled 1st order differential equations, whereas in Lagrangian system, your equation of motion would be 1 2nd order differential equation (per degree of freedom). You can quite easily calculate the kinetic and potential energies, and subsequently get your equations. Now the problem is to get a solution of these, because nobody is interested in the equation of motion of a comet, but rather in its trajectory -preferentially as a function of time and in an intuitive coordinate system. Hamilton equation system is easier to attack. Problems that can be analytically solved (i.e, you get an exact mathematical function for given parameters) are quite limited and problems without an analytic solution need not be very complex (see as an example). This is why I try not to forget birthdays of my friends from computer science. To be able to tell when there will be a solar eclipse you need to employ some approximations. A typical way of doing it is by integrating your equation system with small time steps starting with the initial conditions, which is easy to do with 1st order differential equations.

Tunc


(published on 05/21/2015)

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