Next Direction in Advanced Mechanics?

In summary, the person is currently pursuing a BS in Mechanical Engineering at Cal Poly Pomona and has questions about personal direction in the study of mechanics, specifically in the area of dynamics and systems. They mention that in order to graduate, they need a thorough knowledge of 2D mechanics and systems, with limited knowledge in the 3D case. They also mention studying advanced methods like Lagrangian and Hamiltonian mechanics, but feel they need more understanding in areas like calculus of variations. They ask for recommendations on books or study sites and mention being open to purchasing textbooks. Another forum member recommends a book that covers advanced topics and chaotic systems.
  • #1
cmmcnamara
122
1
Hi all,

I am currently pursuing a BS in Mechanical Engineering at Cal Poly Pomona and I have a few questions regarding some personal direction in the study of mechanics, mostly around the area of dynamics and systems.

In order to graduate from CPP with a BS in ME the only considerations for dynamics are a thorough knowledge of 2D mechanics and systems and a very limited one of those in the 3D case. However I tend to do a lot of additional study on my own which sometimes wanders into graduate school territory.

I've been looking lately a lot of advanced methods for mechanical analysis such as Lagrangian and Hamiltonian mechanics but I also realize I'm quite a ways from really understand what is going on (even mathematically) with those methods. So I am curious if someone could point me in the right direction for some books I could self-study leading to those more advanced topics. I currently have an excellent grasp on analytic calculus methods and differential equation applications (ODE's only) but there also seems to be a need to understand something calculus of variations which I am not familiar with.

So can anyone recommend some books or study sites? I am not opposed to purchasing textbooks either, knowledge comes at a cost.
 
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  • #2
Hey cmmcnamara and welcome to the forums.

I have this book myself, and it covers a lot of the stuff you are mentioning while going very deep into the more advanced topics as well as issues regarding chaotic systems:

https://www.amazon.com/dp/0201657023/?tag=pfamazon01-20

If you can get a table of contents, you should decide whether this suits your needs.
 

Related to Next Direction in Advanced Mechanics?

1. What is the current state of advanced mechanics research?

The current state of advanced mechanics research is constantly evolving and advancing. Some of the recent developments in this field include the use of advanced materials, such as carbon nanotubes and graphene, to create stronger and more lightweight structures. Additionally, there is a growing focus on incorporating computational methods, such as finite element analysis, into advanced mechanics research.

2. What are the potential applications of advanced mechanics?

Advanced mechanics has a wide range of potential applications in various industries, including aerospace, automotive, and biomedical. Some specific applications include designing lightweight and durable materials for aircraft and vehicles, developing new surgical tools and techniques, and creating more efficient and robust machinery.

3. How is advanced mechanics related to other branches of science?

Advanced mechanics is closely related to other branches of science, such as physics, materials science, and computer science. It combines principles from these fields to study the behavior of materials and structures under different conditions. For example, understanding the properties of different materials at a microscopic level is essential in advanced mechanics research.

4. What are some current challenges in advanced mechanics research?

One of the main challenges in advanced mechanics research is the development of accurate and reliable computational models. These models are crucial in predicting the behavior of complex structures and materials, but they often require a significant amount of time and resources to create. Additionally, the use of advanced materials in real-world applications also poses challenges, such as scalability and cost-effectiveness.

5. What can we expect in the future of advanced mechanics research?

In the future, we can expect to see even more advancements in advanced mechanics research. This may include the development of new materials with unprecedented properties, the use of artificial intelligence and machine learning in computational models, and the integration of advanced mechanics principles into everyday objects. Additionally, there may be a stronger focus on sustainability and environmentally-friendly solutions in this field.

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