Is the Approach for Verifying Lagrangian Acceptable?

In summary, the article discusses the validity of a specific approach for verifying Lagrangian formulations in physics. It evaluates the methodology, its theoretical foundations, and practical implications, highlighting potential limitations and areas for improvement. The analysis aims to determine whether the existing techniques effectively ensure the accuracy and reliability of Lagrangian models in various applications.
  • #1
Mishal0488
18
1
TL;DR Summary
Looking for an opinion on a derivation of a Lagrangian mechanics problem I am solving.
Hi Guys

Please refer to the attached document for my derivation.
The image presents the system in plan view, I know one my think that it is unstable structure based on a single pinned connection however this is a simplification of a complex structure sitting on a slew bearing.

Gravity does not play a part in this system. The rod essentially rotates with it's center of mass at l2, there is also a spring connected to the system which will impact into a wall. The system assumes that the spring and wall are already in contact.

Note that the D term is the damping of the system.

Is the approach I have used acceptable?
 

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  • #2
240223.png

In the last line you posutulate that the spring shrinks keeping the shape of arc .　Further,
[tex] U=\frac{1}{2}kl_1^2(\theta-\theta_0)^2[/tex]
for
[tex]\theta-\theta_0 <0 [/tex]
otherwise 0 where ##l_1\theta_0## is natural length of arc shape spring.
 
Last edited:

FAQ: Is the Approach for Verifying Lagrangian Acceptable?

What is the Lagrangian approach in scientific verification?

The Lagrangian approach in scientific verification refers to a method used in physics and engineering where the focus is on tracking individual particles or elements as they move through space and time. This approach contrasts with the Eulerian method, which examines specific locations in the space through which particles move. The Lagrangian method is often used in fluid dynamics, meteorology, and other fields to understand the behavior of systems over time.

Why is verifying the Lagrangian approach important?

Verifying the Lagrangian approach is crucial because it ensures the accuracy and reliability of models and simulations that use this method. Accurate verification helps in predicting physical phenomena correctly and in making informed decisions based on these predictions. Without proper verification, the results derived from the Lagrangian approach could be misleading or incorrect, potentially leading to significant errors in scientific and engineering applications.

What are the common methods used for verifying the Lagrangian approach?

Common methods for verifying the Lagrangian approach include analytical solutions, benchmark problems, and comparison with experimental data. Analytical solutions involve solving simplified versions of the problem to obtain exact results, which can then be compared with the Lagrangian model. Benchmark problems are well-established test cases with known solutions used to validate the approach. Comparing with experimental data involves using real-world measurements to ensure the model accurately represents observed phenomena.

What challenges are associated with verifying the Lagrangian approach?

Challenges in verifying the Lagrangian approach include dealing with complex boundary conditions, ensuring numerical stability, and managing computational resources. Complex boundary conditions can make it difficult to obtain accurate solutions, while numerical stability issues can arise from the discrete nature of computational methods. Additionally, Lagrangian simulations often require significant computational power, especially for large-scale problems, making efficient resource management essential.

How can the reliability of the Lagrangian approach be improved?

The reliability of the Lagrangian approach can be improved by using higher-resolution models, implementing advanced numerical techniques, and continuously validating the approach against new experimental data. Higher-resolution models can capture finer details of the system being studied, while advanced numerical techniques can enhance accuracy and stability. Ongoing validation against experimental data ensures that the approach remains accurate and relevant as new information and technologies become available.

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