Lagrangian, Hamiltonian coordinates

In summary, the speaker has a strong understanding of Newton's laws and momentum principles in Classical Mechanics but lacks exposure to Lagrangian and Hamiltonian methods. They are struggling with problems involving coordinate systems, specifically in relation to a disk rolling on an inclined plane with a pendulum attached. They are seeking guidance on what prerequisites they need to solve these types of problems and are open to suggestions for reading material or resources. An introductory text on analytical mechanics, such as Fowles' "Analytical Mechanics," is recommended for guidance on how to move between generalized and cartesian coordinates in solving these types of problems.
  • #1
badri89
13
1
Dear All,

To give a background about myself in Classical Mechanics, I know to solve problems using Newton's laws, momentum principle, etc.

I din't have a exposure to Lagrangian and Hamiltonian until recently. So I tried to read about it and I found that I was pretty weak in coordinate systems. Especially in problems such as, a disk rolling on a inclined plane with a pendulum attached to it. I find much difficulty in finding the coordinates of the bob.

What prerequisite I need to crack these sort of problems? Give me some links to brush up coordinate system or suggest some reading! Thanks
 
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  • #2
Any introductory text on analytical mechanics should provide adequate guidance - they all have to move between the "generalized" coordinates that are natural to a problem and the cartesian coordinates where you know how to express the kinetic energy.

For example, Fowles "Analytical Mechanics" is a good undergraduate text.
 

1. What are Lagrangian and Hamiltonian coordinates?

Lagrangian and Hamiltonian coordinates are two different mathematical approaches used to describe the motion of particles or systems in physics. They are both based on the principle of least action, which states that the actual path taken by a particle or system is the one that minimizes the action integral.

2. What is the difference between Lagrangian and Hamiltonian coordinates?

The main difference between Lagrangian and Hamiltonian coordinates is the form of the equations used to describe the motion. Lagrangian coordinates use the Lagrangian function, which is a function of the position and velocity of the particles, while Hamiltonian coordinates use the Hamiltonian function, which is a function of the position and momentum of the particles.

3. How are Lagrangian and Hamiltonian coordinates useful in physics?

Lagrangian and Hamiltonian coordinates are useful in physics because they provide a way to describe the motion of particles and systems in a mathematical and systematic manner. They also allow for the easy application of the principle of least action, making it possible to find the equations of motion for a wide range of physical systems.

4. What are the advantages of using Lagrangian and Hamiltonian coordinates?

One advantage of using Lagrangian and Hamiltonian coordinates is that they can simplify the equations of motion for complex systems, making them easier to solve. They also provide a more elegant and intuitive approach to describing the behavior of physical systems compared to traditional methods.

5. Are Lagrangian and Hamiltonian coordinates used in any other fields besides physics?

Yes, Lagrangian and Hamiltonian coordinates are used in other fields besides physics, such as engineering, mechanics, and control theory. They are also used in economics and finance, where they are used to model and analyze complex systems and their behavior.

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