The Lagrangian and the second derivative?

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Thread starter filip97
Start date Feb 3, 2019
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Derivative Lagrangian Second derivative

In summary, the Lagrangian is a mathematical function used in classical mechanics to describe the dynamics of a physical system. Its significance lies in its ability to provide a more elegant and concise description of a system's dynamics compared to traditional Newtonian formulation. The second derivative of the Lagrangian is used to derive the equations of motion for the system, known as the Euler-Lagrange equations. These equations can also be used to find the path that a system will follow in order to minimize the action. The Lagrangian can also be applied in other fields such as quantum mechanics, quantum field theory, and economics and finance to describe and derive important equations and principles.

Feb 3, 2019

filip97

Why Lagrangian not depend of higher derivatives of generalised coordinates ?

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Feb 3, 2019

weirdoguy

Sometimes it depends, eg in general relativity or in elastomechanics. In most cases it does not, but there is no deeper explanation for that.

EDIT: AFAIK in QFT it would lead to inconsistencies, but I don't remember details.

Last edited: Feb 3, 2019

1. What is the Lagrangian?

The Lagrangian is a mathematical function used in classical mechanics to describe the dynamics of a physical system. It is defined as the difference between the kinetic and potential energies of the system.

2. What is the significance of the Lagrangian?

The Lagrangian is significant because it allows us to describe the motion of a system using a single equation, known as the Euler-Lagrange equation. This equation can be used to find the path that a system will take in order to minimize the action, which is a fundamental quantity in classical mechanics.

3. What is the second derivative in relation to the Lagrangian?

The second derivative, also known as the second order derivative, is a mathematical concept used in calculus to describe the rate of change of a function. In the context of the Lagrangian, the second derivative is used to determine the stability of a system and to predict its behavior over time.

4. How is the Lagrangian used in physics?

The Lagrangian is used in physics to describe the motion of a system, such as a particle or a collection of particles, in terms of its position, velocity, and acceleration. It is a fundamental tool in classical mechanics and is also used in other areas of physics, such as quantum mechanics and field theory.

5. Can the Lagrangian be applied to any physical system?

Yes, the Lagrangian can be applied to any physical system, as long as it follows the laws of classical mechanics. It is a general and versatile tool that has been successfully used to study a wide range of systems, from simple pendulums to complex systems such as planets in orbit.