Interesting book explaining the principle of least action in detail

In summary, the conversation discusses the difficulty of understanding the concept of mechanics being taught as mathematics instead of physics. A recommendation is made for a book on classical mechanics that explains the principle of least action and its history. It is also suggested to have a strong understanding of vector calculus in order to understand the material in the book.
  • #1
Isolde
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Hi, I'm doing further maths and I would like to study maths at university. I have been asked to read a number of books to put on my personal statement, and as I am finding it difficult coming to terms with the fact that mechanics is taught as maths and not physics, a maths don at Oxford suggested that I should look into the principle of least action, apparently what all mechanics is based on (I'm sure that it's fairly obvious that I know nothing about this, so forgive me if I'm wrong). I was wondering if anyone knew of a readable book that explains the concept and the history surrounding it that I could read. Thanks!
 
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  • #2
I would highly recommend Taylor's book on classical mechanics:

https://www.amazon.com/gp/product/189138922X/?tag=pfamazon01-20

You'll have to read the chapter on Variational Calculus and then the chapter on Lagrangian Mechanics. Once you understand those, the variational principle will make sense.

However, keep in mind that you'll need to have a solid grasp of vector calculus in order to understand the material in Taylor. Personally I learned vector calculus from this text:

https://www.amazon.com/gp/product/1429215089/?tag=pfamazon01-20

Naturally, in order to understand vector calculus you first need to understand regular old single variable calculus. Though on that subject I know of no good introductory books, because personally I was taught basic calculus by a weekly private tutor, and then I skipped straight to advanced texts like Spivak:

https://www.amazon.com/gp/product/0914098918/?tag=pfamazon01-20

But Spivak definitely isn't for beginners.
 
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1. What is the principle of least action?

The principle of least action is a fundamental concept in physics that states that the motion of a system between two points will follow a path that minimizes the action, which is defined as the integral of the system's Lagrangian over time.

2. Why is the principle of least action important?

The principle of least action is important because it provides a mathematical framework for understanding and predicting the behavior of physical systems. It is also a fundamental principle that is used in various fields of physics, including classical mechanics, quantum mechanics, and field theory.

3. Can you give an example of the principle of least action in action?

One example of the principle of least action in action is the motion of a pendulum. The pendulum will follow a path that minimizes the action, which is the integral of its Lagrangian over time. This results in the pendulum oscillating with a specific frequency and amplitude.

4. How does the principle of least action relate to other principles in physics?

The principle of least action is related to other principles in physics, such as the conservation of energy and the principle of stationary action. These principles all stem from the fundamental concept of minimizing action to describe the behavior of physical systems.

5. Are there any real-life applications of the principle of least action?

Yes, there are several real-life applications of the principle of least action. It is used in various fields of physics, such as in the study of fluid dynamics, electromagnetism, and quantum mechanics. It also has applications in engineering, such as in the design of efficient systems and optimization problems.

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