Is action-reaction contained in the Lagrangian

  • Thread starter aaaa202
  • Start date
  • Tags
    Lagrangian
In summary, the conversation discusses the derivation of conservation laws from the Lagrangian, and the question of why the Lagrangian incorporates action-reaction. The speaker mentions that the Lagrangian can be used for an arbitrary number of particles and that linear momentum can be shown to be conserved from translational invariance. However, the principle of stationary action does not necessarily require action and reaction. The conversation also briefly touches on the idea that, with certain assumptions, the Lagrangian can be shown to have similar properties in classical physics.
  • #1
aaaa202
1,169
2
A lot of conservation laws are derived from the lagrangian in my book. However, I fail to see why the Lagrangian incorporates action-reaction. Since it works for an arbitrary amount of particles and linear momentum can be show to be conserved from translational invariance it must do so.
But deriving it from the principle of stationary action, doesn't really have any assumption that action must have a reaction as far as I can see it.
What do I fail to see?
 
Physics news on Phys.org
  • #2
With some assumptions about the shape of the Lagrangian and in classical physics, it can be shown similar to that.

In the general case, you do not have a conserved total momentum - just look at a pendulum as example.
 

Related to Is action-reaction contained in the Lagrangian

1. What is the concept of action-reaction in physics?

The concept of action-reaction, also known as Newton's Third Law of Motion, states that for every action, there is an equal and opposite reaction. This means that when a force is applied to an object, the object exerts an equal and opposite force back onto the source of the force.

2. How is action-reaction related to the Lagrangian?

The Lagrangian, named after the mathematician Joseph-Louis Lagrange, is a function used in classical mechanics to describe the dynamics of a system. It is derived from the principle of least action, which states that the path taken by a system between two points in time is the one that minimizes the action. As a result, the principle of least action is related to the concept of action-reaction, as the forces involved in the system must balance out for the action to be minimized.

3. Is action-reaction always contained in the Lagrangian?

In classical mechanics, the Lagrangian does not explicitly include the concept of action-reaction. However, as the principle of least action is based on the conservation of energy and momentum, action-reaction can be seen as a consequence of these conservation laws being contained in the Lagrangian. In other words, while action-reaction may not be explicitly stated in the Lagrangian, it is still a fundamental aspect of the dynamics described by it.

4. Can the Lagrangian be used to describe action-reaction in all systems?

The Lagrangian is a powerful tool in classical mechanics and can be used to describe a wide range of systems, including those involving action-reaction. However, there may be cases where the Lagrangian is not suitable or may not accurately describe the dynamics of a system. In these cases, other methods, such as Hamiltonian mechanics, may be used to better describe the system.

5. How does the inclusion of constraints affect the action-reaction principle in the Lagrangian?

In some cases, a system may have constraints, such as fixed boundaries or objects, that restrict the motion of the system. In these cases, the principle of least action may still hold true, but the constraints must also be taken into account when deriving the Lagrangian. This means that the action-reaction principle may be slightly modified, but it is still a fundamental aspect of the dynamics of the system.

Similar threads

I Proving that the Lagrangian of a free particle is independent of q
Replies
1
Views
631
I Why isn't the Lagrangian invariant under ##\theta## rotations?
Replies
5
Views
967
I Spatial homogeneity condition for a free particle Lagrangian
2
Replies
48
Views
516
I Types of symmetries in Lagrangian mechanics
Replies
3
Views
1K
I Do action force and reaction force lie on same line?
Replies
4
Views
1K
Why is Hamilton's Principle assumed to be valid for non-holonomic systems?
Replies
25
Views
2K
I What is the expected result of plugging equations of motion into the Lagrangian?
Replies
1
Views
1K
I Why is the 'motionless solution' not always valid in classical mechanics?
Replies
12
Views
1K
A The tautological 1-form: Lagrange vs. Hamilton formalism
Replies
27
Views
2K
A Exploring Why Hamilton's Principle Uses L=KE-PE Lagrangian
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top