Maximizing Symmetry in Lagrangian for a Particle in 3D Cylindrical Coordinates

In summary, the conversation discusses finding a symmetry for the lagrangian of a particle in 3D cylindrical coordinates with a potential energy function dependent on r and k.theta+z. The attempted solution involves using r, theta, and u=k.theta+z as generalized variables and applying the Lagrange formalism to utilize the identified symmetry.
  • #1
noor
4
0

Homework Statement



the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates.
I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z
V=V(r,k.theta+z)


Homework Equations



k is constant
L=T-V
T is kinetic energy

The Attempt at a Solution


i tried to find translational symmetry
r --> r+s
theta --> theta-s/k
im not sure any help please ?
 
Physics news on Phys.org
  • #2
I'm not through with checking this example, but it looks as if it could be a good idea to use
[itex]r[/itex], [itex]\theta[/itex], and
[tex]u=k \theta + z[/tex]
as the generalized variables and then perform the Lagrangeformalism. It's easy to see that with this choice of variables you make use of the very symmetry you've already identified!
 

FAQ: Maximizing Symmetry in Lagrangian for a Particle in 3D Cylindrical Coordinates

What is Lagrangian and how is it used in physics?

Lagrangian is a mathematical formulation used in classical mechanics to describe the dynamics of a system. It is a function that summarizes the equations of motion of a system in terms of position, velocity, and time. It is used to determine the most probable path that a system will take between two points in its configuration space.

What is the principle of least action and how is it related to Lagrangian?

The principle of least action states that a physical system will always follow the path that minimizes the action, which is the integral of the Lagrangian over time. This principle is related to Lagrangian because the Lagrangian is used to calculate the action of a system and determine the path that minimizes it.

What is the importance of symmetry in Lagrangian mechanics?

Symmetry plays a crucial role in Lagrangian mechanics because it allows for the simplification of equations of motion. A system that exhibits symmetry will have conserved quantities, which are important in understanding the behavior of the system. Additionally, the symmetries of a system can be used to derive new equations of motion.

How does Noether's theorem relate to Lagrangian and symmetry?

Noether's theorem states that for every continuous symmetry in a system, there exists a corresponding conserved quantity. This means that symmetries in a system are directly related to conserved quantities, which are determined by the Lagrangian. Noether's theorem is a powerful tool for understanding the dynamics of a system and is closely linked to Lagrangian and symmetry.

What are some examples of systems where Lagrangian and symmetry are used?

Lagrangian and symmetry are used in a wide range of physical systems, including classical mechanics, electromagnetism, quantum mechanics, and general relativity. Some specific examples include the motion of planets in our solar system, the behavior of particles in a magnetic field, and the dynamics of fluids. They are essential concepts in many areas of physics and are continuously being applied to new systems and problems.

Similar threads

What is the Fermion's mass in this Lagrangian?
Replies
0
Views
1K
Determine the Lagrangian for the particle moving in this 3-D cos^2 well
Replies
6
Views
1K
Using Lagrangian to show a particle has a circular orbit
Replies
4
Views
2K
Find Symmetry for Lagrangian in 3D Cylindrical Coordinates
Replies
2
Views
1K
Lagrangian for a particle in a bowl with parabolic curvature
Replies
10
Views
5K
Question about using the Lagrangian for a spinning rubber band problem
Replies
25
Views
3K
Plane pendulum: Lagrangian, Hamiltonian and energy conservation
Replies
6
Views
2K
Lagrangian Mechanics Question: A Yoyo radius a and b
Replies
1
Views
2K
I Types of symmetries in Lagrangian mechanics
Replies
3
Views
1K
Lagrangian mechanics, system of a spring and a pendulum
Replies
21
Views
4K

Hot Threads

Recent Insights

Back
Top