Lagrangian Mechanics For The Non-Physicist Book

Learn Lagrangian Mechanics The Right Way – Even If You’re A Beginner

Anyone who truly wants to understand general relativity, quantum field theory or any other area of modern physics first needs to master Lagrangian mechanics. Lagrangian mechanics is the framework used to describe all of modern physics.

The issue with most resources teaching Lagrangian mechanics is that they don’t truly teach you the why behind it – all they do is give you another approach for solving made-up mechanics problems. But what if it didn’t have to be this way? What if you could truly learn Lagrangian mechanics the right way?

The good news is that this book will do exactly that for you. It will take you on a journey through the very fundamentals, theory, mathematics and advanced applications of Lagrangian mechanics. You’ll learn Lagrangian mechanics in a completely unique way you’ve likely never seen before.

Lagrangian Mechanics For The Non-Physicist

Paperback & hardcover versions

$29.95

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Lagrangian Mechanics & Field Theory: A Complete Course

Lagrangian Mechanics For The Non-Physicist (eBook)
Field Theory For The Non-Physicist (eBook) – included as part of the course, this book is a direct continuation of Lagrangian Mechanics For The Non-Physicist that dives much deeper into modern physics and topics like quantum field theory
Worksheets with solved practice problems
Bonus resources & tutorials

$49.95

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The Truth About Lagrangian Mechanics…

Anyone studying general relativity, quantum field theory or really any other advanced topic in physics will inevitably come across Lagrangian mechanics.

Trying to understand physics at a deep level without understanding Lagrangian mechanics is like driving a car without a steering wheel – you’ll eventually run into a wall and not be able to move forward anymore.

The issue is that Lagrangian mechanics is often taught in a very abstract way without really giving you the true why behind it, leaving you wondering “what am I ever going to do with this stuff?”

Most resources you’ll find will cover Lagrangian mechanics with the approach of treating it as just a more elegant way to solve some made-up mechanics problem that Newton’s laws could have solved anyway.

However, this approach is missing the point – Lagrangian mechanics is not just a tool for solving an arbitrary problem in a problem set.

The true reason why Lagrangian mechanics is so incredibly powerful is that it gives you a general framework for describing literally any area of modern physics.

THIS is the reason why Lagrangian mechanics exists and almost no one will teach you it this way…

Whether you want to learn:

Electrodynamics
Special and general relativity
Quantum field theory
String theory

You absolutely need to have a deep understanding of Lagrangian mechanics to even get started on any of these topics.

For myself, learning Lagrangian mechanics was the biggest catalyst that enabled me to understand high-level physics and I believe it will be for you too.

Today, I can confidently say that learning Lagrangian mechanics was the single most important thing I ever did in terms of my physics education.

However, if there is one thing I wish I would’ve had back when I first began learning it, it would be a dedicated resource that introduces Lagrangian mechanics completely from scratch and gives you everything in one place.

This is exactly what this book provides you with.

You’ll learn Lagrangian mechanics in a completely unique way you’ve likely never seen before – as both a fundamental framework related to advanced modern physics, but also as an incredibly powerful problem solving tool.

Lagrangian Mechanics For The Non-Physicist is a complete resource specifically designed to teach you everything you’d possibly need to know about Lagrangian mechanics – the fundamentals, prerequisites, theory, math and practical applications. It’s all here.

Yes, I’m Interested!

What This Book Can Do For You

I was a beginner on Lagrangian mechanics not too long ago. Now after learning it through the years, I understand exactly what I would have needed back then and what I believe you will as well.

Learn real physics, beyond popular science

Understand high-level ideas and methods underlying most areas of modern physics (electrodynamics, relativity, field theory and many more), so that you’ll have a much deeper understanding of physics than most people will ever have.

Understand advanced physics textbooks

Gain the necessary skills, knowledge and practical tools to pick up and understand any advanced physics textbook that talks about Lagrangian mechanics (that is, nearly any textbook on modern physics).

Save time and money on learning

This is the last book you’ll ever need on Lagrangian mechanics. And better yet, it will teach you the actually useful stuff in a fraction of the time.

Here’s Exactly What You Get:

The book is structured in logically ordered chapters that each cover a particular aspect of Lagrangian mechanics.

In total, the book includes:

Pages worth of unique material formatted in a very logical and easy-to-follow way

Unique, detailed illustrations and diagrams to provide visualizations for many difficult concepts

The first chapter covers all the basic concepts needed moving forward, such as mass, energy, momentum and equations of motion.

This chapter also covers Newton’s laws and the general problem solving methods in Newtonian mechanics.

More importantly, however, we look at the main issues with Newtonian mechanics, which works as motivation for introducing the Lagrangian formulation in the first place.

In this chapter, Lagrangian mechanics is introduced in a very intuitive manner. We look at why Lagrangian mechanics is useful and what it’s based on, without yet getting into the details.

This chapter will give you the big picture behind Lagrangian mechanics, which the latter chapters of the book will then expand on in MUCH greater detail.

Calculus of variations is the area of math Lagrangian mechanics and a lot of other areas of physics like field theory, is largely based on.

In this chapter, you’ll learn the most important concepts in variational calculus like functionals, the Euler-Lagrange equation, the Beltrami identity, Lagrange multipliers and constrained optimization.

We also look at various examples and applications of variational calculus, such as describing motion of light rays in the field of optics, deriving geodesics in differential geometry as well as some famous physics problems like the brachistochrone and the catenary problem.

Lastly, we connect everything we’ve learnt about calculus of variations throughout this chapter directly to Lagrangian mechanics – this gives you all the mathematical tools you’ll need to really understand Lagrangian mechanics deeply.

In this chapter, we’ll dive deep into the main topics related to Lagrangian mechanics as well as how to apply it in practice.

The following are just a few topics we will cover here:

Solving problems using Lagrangian mechanics (general strategies and lots of examples)
Generalized coordinates and momenta
Constrained dynamics and Lagrange multipliers

In this chapter, we dive deeper into the theoretical as well as some practical aspects of Lagrangian mechanics.

The main goal of this chapter is to generalize various familiar concepts in mechanics like forces and work to work in the Lagrangian formulation.

In particular, we will look at:

The concept of generalized forces and virtual work
Incorporating friction and non-conservative forces into the Lagrangian formulation
Dealing with velocity-dependent potentials and forces
The principle of virtual work and how this allows us to solve statics problems in Lagrangian mechanics
D’Alembert’s principle and how it provides a direct link between Newton’s laws and Lagrangian mechanics

The link between symmetries and conservation laws is perhaps the most important discovery about modern physics Lagrangian mechanics allows us to make.

This chapter of the book is about exactly that – we look at symmetries of Lagrangians, cyclic coordinates, how conservation laws come about in Lagrangian mechanics and Noether’s theorem.

We also look at how symmetries and conservation laws arise through the Lagrangian formulation in other interesting contexts related to modern physics. Examples of this include the relativistic conservation of energy and the conservation of probability in quantum mechanics.

In the Appendices, you’ll find reviews of some important mathematical concepts, such as coordinate systems.

Also, many of the chapters contain calculations that are just way too long to include inside the main content and would make the chapters too convoluted. These calculations are included in detail in the Longer Calculations -section at the end of the book.

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What Others Have Said About The Book & Course:

Easily one of the best resources I’ve ever come across

“Easily one of the best resources on Lagrangian mechanics I’ve ever come across. What I find most fascinating is the unique angle the course takes in connecting topics in Lagrangian mechanics to areas like relativity.

Honestly, I didn’t really understand much about Lagrangian mechanics (but had tried to) until taking this course nor did I realize how important it is everywhere else in physics. The course material is explained so clearly that I’m actually surprised how easy physics could be. I even got some new insights about topics I was already familiar with, for instance, the part about Newton’s laws helped me understand why Newton’s 1st and 3rd laws are necessary.

The practice problems were also incredibly valuable in helping the concepts stick with me. Looking forward to the rest of the material being added!”

Marcus

I’m so glad I took the chance to sign up

“Thank you for creating such a helpful course! I’m so glad I took the chance to sign up. The way the topics were presented made them seem so easy and enjoyable to learn. Since working through the first few parts, I’ve been able to actually understand the Lagrangian mechanics parts in my QFT For The Gifted Amateur -textbook. I owe it all to this course!”

Noah

This was different

“I must say, I’m super happy I bought the book and I’m really impressed with the quality and depth of understanding it’s given me. I’ve read other books in the past that left me even more confused, but this one was different. Overall, I can’t recommend it enough. This has exceeded all my expectations and has given me a solid foundation in Lagrangian mechanics.”

Emma

Changed everything for me!

“Happy to provide my review for your Lagrangian course. Before this course, I had heard of Lagrangian mechanics and knew it was important for many other areas of physics, but I just couldn’t get past all the abstract theory. I tried looking it up from Wikipedia, but it was way too much for me. However, this course changed everything for me. I found the lessons so easy and interesting to follow and I finally began understanding how Lagrangian mechanics actually works. I think where this course really excels is in connecting Lagrangian mechanics to other physics concepts and explaining why you need to learn them. And of course, also in teaching them. Would absolutely recommend this to anyone who wants to improve their understanding of Lagrangian mechanics and physics in general!”

Aiden

Some Samples From Inside The Book:

Frequently Asked Questions

This book is definitely for you if you have a basic understanding of high-school level math. This includes vector operations, trigonometry, basic calculus and possibly taking some partial derivatives.

You should also be familiar with some elementary physics concepts, such as velocity, forces and energy, however, there will be a brief review of all these concepts in the first chapter of the book as well.

Lagrangian mechanics is definitely not an easy topic, but with the above-mentioned prerequisites, you should be able to do well.

Each new topic is covered from scratch and I’ve also tried to cover everything in a way that doesn’t require you to know much beforehand.

So, all the advanced stuff in the book is built on the previous things you learn.

However, if you find a particular topic challenging, the beauty of a book like this is that you can take as much time as you need to learn something and then continue with the reading.

The book Lagrangian Mechanics For The Non-Physicist includes just the book itself, a physical version of it (paperback or hardcover). This book is a great choice if you just want to read through the material.

The full Lagrangian Mechanics & Field Theory: A Complete Self-Study course, on the other hand, automatically includes digital versions of the Lagrangian mechanics book and my other book on relativistic field theory.

This full course also includes solved pre-reading assignments, worksheets, bonus material and other stuff and is overall organized into a more structured learning experience. However, the main content is still based on the books, so getting just the books will certainly teach you all the important stuff.

The course is for you if you want a more structured approach to your learning and be able to work through practice problems yourself, but fundamentally, the book and the course will both teach you the same concepts.

Of course, you can always start by getting just the book, and if later on you feel like you want even more, you can just upgrade to the course. If you’ve bought the book and would like to upgrade to the full course, just send me an email to ville@profoundphysics.com and I’ll give you a discount on it!

Field Theory For The Non-Physicist is my second book, which covers relativistic field theory and many topics in modern physics related to it – electromagnetism as a field theory, gauge theories, interaction theory, the Higgs mechanism and many many more.

The field theory book is a direct continuation of this Lagrangian mechanics book, a part two of it if you will. It will take everything covered in the Lagrangian mechanics book and build upon it to provide you a really deep understanding of many crucial concepts in modern physics.

While I haven’t specified any absolute prerequisites for this book to get the most out of it, you may want to have a basic understanding of high-school level math and physics, which includes basic vector operations, trigonometry, single-variable calculus and some partial derivatives.

If you don’t feel comfortable in your skills on these topics, you might want to take a look at my Advanced Math For Physics -course first. The course will teach you all the math prerequisites from the ground up. You’ll find more information about it on this page.

With the above elementary prerequisites, you should be able to do well. While some of the topics covered are definitely advanced, all the necessary prerequisites should already be inside the book.

If you run into any trouble or simply have additional questions you want clarified, please contact me at ville@profoundphysics.com. I’ll be happy to help!

Yes! If you’re a student or teacher, just contact me at ville@profoundphysics.com using your student/teacher email address.

I’m also willing to discuss any bulk discounts in case you would like to get multiple books, say for a class or some other purpose (either digital or physical versions).

What are you waiting for?

This is exactly the resource I wish I had back when I first began learning Lagrangian mechanics – and you can have it today!

Let’s Do It!