# Newtonian mechanics VS. variational principles

## Is the text true from beginning to end?

1 vote(s)
100.0%
2. ### no

0 vote(s)
0.0%
1. Jan 22, 2008

### fortaq

Hello!

Would you say that the following text is true from beginning to end?:

-----------------------
Basically, there are two mechanical approaches to describe a particle: (a) the variational principles (e.g., the Lagrangian and Hamiltonian ones) and (b) the Newtonian approach. The former approaches in principle deal with the determination of an equation of motion from a function of energy terms. In contrast to these methods, in the Newtonian approach the equation of motion $$\dot{\textbf{p}}=\textbf{F}$$ of a particle is established directly, where $$\textbf{F}$$ is the force on the particle and $$\dot{\textbf{p}}$$ is the particle's change in momentum, also called resulting force. From this equation we can then derive several parameters, e.g., the energy terms of the particle.
-----------------------

best wishes, fortaq

2. Jan 22, 2008

### JukkaVayrynen

My understanding is that Lagrangian and Newtonian dynamics are very close to each other, Lagrangian just uses the fact that internal forces of the system don't affect the motion. Hamiltonian dynamics, based on the principle of variation, is something much more fundamental than the other two.

3. Jan 22, 2008

### fortaq

Thanks for response.
Could you give a reference to a textbook? I thought that Lagrangian and Hamiltonian mechanics are in principle the same and both are variational principles.