Exploring Higher-Order Lagrangian Systems with Physical Relevance

In summary, higher-order Lagrangian systems involve derivatives of coordinates and velocities in the Lagrangian function, leading to higher-order differential equations. Exploring these systems allows for better understanding and modeling of complex physical systems. Physical relevance can be determined by analyzing equations of motion and comparing them to known laws and principles. Examples include charged particles in electromagnetic fields and pendulums with moving supports. Higher-order Lagrangian systems can be solved using mathematical techniques such as perturbation theory, numerical methods, or symmetry analysis.
  • #1
Omega137
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Hello!

I`m looking for Lagrangian Systems with Lagrangian function containing higher derivatives in t. I would be really happy if someone can tell some higher order Lagrangians with physical relevance.

Thanks, Viktor
 
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  • #2


Is there about your question that relates specifically to relativity? If not, then you will probably get better answers if we move this question to the Beyond the Standard Model forum.

-Ben
 

1. What are higher-order Lagrangian systems?

Higher-order Lagrangian systems refer to systems that involve derivatives of the coordinates and velocities in the Lagrangian function. This means that the equations of motion are higher-order differential equations. These systems often arise in physics when considering more complex and realistic scenarios.

2. What is the significance of exploring higher-order Lagrangian systems?

Studying higher-order Lagrangian systems allows us to better understand and model physical systems that involve more complex dynamics and interactions. This can lead to more accurate predictions and explanations of real-world phenomena.

3. How do we determine the physical relevance of a higher-order Lagrangian system?

The physical relevance of a higher-order Lagrangian system is determined by analyzing its equations of motion and comparing them to known physical laws and principles. This involves examining the system's energy, momentum, and other conserved quantities, as well as considering the system's behavior in different scenarios.

4. What are some examples of higher-order Lagrangian systems with physical relevance?

One example is the motion of a charged particle in an electromagnetic field, which involves both the position and velocity of the particle in the Lagrangian function. Another example is the motion of a pendulum with a moving support, which involves higher-order derivatives of the angle and angular velocity in the Lagrangian function.

5. How can we solve higher-order Lagrangian systems?

Solving higher-order Lagrangian systems typically involves using mathematical techniques such as perturbation theory, numerical methods, or symmetry analysis. These approaches can help us understand the behavior of the system and make predictions about its future motion.

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