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 course will do exactly that for you. You’ll get lifetime access to EVERYTHING – for a one-time price only!

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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 university courses 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… but they should.

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 course will give you.

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 & Field Theory: A Complete Course 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.

Enroll Now – for a discounted price!

(Note; a VAT fee may be added depending on your country)

What This Course 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 resources

This is the last course 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 course is structured in easy-to-navigate parts that each cover a particular aspect of Lagrangian mechanics that even many university courses won’t cover.

In total, the course includes:

Pages worth of unique lesson material in an easy-to-read, downloadable and printable format
Practice problems of varying difficulty, with step-by-step solutions

You’ll get lifetime access to EVERYTHING as well as to all future content added to the course for a one-time price.

Course Contents

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

This part 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 part of the course, 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 part will give you the big picture behind Lagrangian mechanics, which the latter parts of the course 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 part, 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 variational calculus in this directly to Lagrangian mechanics – this gives you all the mathematical tools you’ll need to really understand Lagrangian mechanics deeply.

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

The main goal of this part 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

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

This part of the course 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 in field theories through the Lagrangian formulation. This turns out quite a bit more abstract but incredibly rewarding in the end!

Pretty much all modern theories of physics – including electromagnetism, general relativity and all quantum field theories – are field theories. With all the tools of Lagrangian mechanics we’ve learnt throughout this course, we are now ready to begin studying field theory. This part is for exactly that – to teach you the key ideas of field theory using the Lagrangian formalism.

In this part, we’ll cover various topics ranging from the transition from ordinary particle mechanics to field theory to generalizing Noether’s theorem for field theory.

Throughout, you’ll learn the general framework for constructing field theories and describing them, general rules for building relativistic theories and working with four-vectors and tensors as well as – of course – plenty of examples along the way.

This part is all about applications and examples of everything we’ve learnt about field theory so far.

We dive into various different field theories, including scalar field theories, vector field theories and gauge theories as well as the predictions of each of these theories.

The main theme of this part is looking at how the Lagrangian formulation naturally encodes different properties of fields (and quantum particles), such as mass, charge, polarization and so on.

An important real-world application of this part is looking at electromagnetism as a relativistic field theory and seeing how fundamental properties of electricity and magnetism arise from its Lagrangian field theory description.

Part 9 of the course is all about interactions – how particles interact with various fields and how different fields interact with each other.

In a sense, this part ties everything covered in the earlier parts of the course together with field theory.

For example, we look at how to combine the particle Lagrangian mechanics with the field theory description of electromagnetism, leading us to the description of how charged particles produce electromagnetic fields and how electromagnetic fields create forces. An interesting thing we discover is how electromagnetism would behave much differently if photons had a mass.

We also dive deep into the theory and practical applications of constructing interacting field theories – everything from self-interacting field theories to gauge interactions.

To top off this part, we discuss the phenomena of spontaneous symmetry breaking and the Higgs mechanism – the way in which most elementary particles gain their masses!

Inside the course, there will be various bonus resources on different topics that help you deepen your understanding of Lagrangian mechanics and physics in general.

These bonus resources haven’t been fully planned yet but there will likely be, for example, resources covering orbital mechanics, Hamiltonian mechanics and other topics closely related to Lagrangian mechanics.

There will also be tutorials on various mathematical topics, such as solving differential equations.

Along with all of the above, you also get:

  • Workbook that includes tons of practice problems you can do yourself
  • Solution manual with answers and step-by-step solutions to every problem
  • All content available in downloadable & printable format, along with a mobile app that gives you easy access to all course content on your mobile device
  • Bonus Resources & Tutorials: These haven’t been fully planned yet but there will be bonus resources on at least orbital mechanics and Hamiltonian mechanics
Get Started Today!

What Makes This Course Different?

  • Many other courses will contain arbitrary deadlines and expiration dates that give you unnecessary stress. This course doesn’t do that – you’ll have access to this course forever and you can study completely at your own pace, so this is perfect for busy people.
  • Most other courses will focus too much on using Lagrangian mechanics just for solving arbitrary problems and completely miss out on the true power of the Lagrangian formulation. This course is different in that we focus on what actually makes Lagrangian mechanics useful, beyond just solving arbitrary problems.
  • Many courses and textbooks on Lagrangian mechanics will just throw a bunch of theory at you, after which you then go and solve a few problems – and then forget everything the next day! From this course, you will actually retain the knowledge you gain since each lesson starts with properly motivating why what you learn is important.
  • Most other courses have a very limited curriculum and they leave out topics that are “beyond the scope of this course”. I will never do that. In each lesson, you’ll often find discussions and insights about much more advanced concepts even if they are not directly part of the main lesson topic – this way, you’ll gain an understanding that is vastly deeper than most people will ever have.

What This Course Has Done For Others:

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 lessons 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 took this course and I’m really impressed with the quality and depth of understanding it’s given me. I’ve taken other courses in the past that left me even more confused, but this was different. Overall, I can’t recommend this course enough. It 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 Course:

Frequently Asked Questions

I would say this course is for you, if you have a basic understanding of high-school level math. This includes basic 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 inside the course 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 course is built on the previous things you learn.

However, if you find a particular topic challenging, you can always ask me for resource recommendations on where to learn more about it – the beauty of a self-study course like this is that you can go at your own pace, take as much time as you need to learn something and then continue with the course material.

The most important things you’ll need for this course are an interest to learn new things and a willingness to put in the effort for it!

While I haven’t specified any absolute prerequisites for this course, to get the most out of this course, you might find the course a bit difficult without basic understanding of high-school level math and physics, which includes basic vector operations, trigonometry, single-variable calculus and possibly taking 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 course.

However, if you find your knowledge to be lacking in some area, you can always go and review the topic somewhere and then come back – you have until forever to complete the course!

At the checkout, you’ll enter an email address. After the purchase is completed, you’ll receive an access link to the course dashboard sent to the email you entered.

You’ll then find all the other information and instructions, such as for how to access the course lessons, worksheets and everything else inside the course dashboard – everything should be a walk in the park!

However, if you run into any trouble accessing the course after purchase or you lose access to it somehow, please contact me at ville@profoundphysics.com. I’ll be happy to help!

There isn’t any required time investment for this course. You can go as slowly or as quickly as you choose, so this is perfect if you’re a busy person with a full-time job, family or something similar.

I personally believe that the best learning happens when you’re doing it out of your own will and when you choose to do so. This is a principle I’m also going by with this course – the idea is that you only study when you choose to.

You also get lifetime access to the course, so there are no deadlines and no pressure for you to complete anything, it’s all up to how much you choose to study – no stress involved!

As far as the length of the course, there is in total, 596 pages worth of lesson content and a bunch of practice problems with each lesson.

Assuming you complete all lessons and do all practice problems at an average pace, from my own experience, this would be equivalent to the time frame and workload of about a 12-week-long university course.

But the nice thing is that the pace here is completely up to you, so it might be a 4-week-long course or a 2-year-long course – it all depends on how you want to go about it!

Sure! If you have any questions about the material or something is unclear, just send me an email to ville@profoundphysics.com and I’ll try to get back to you as soon as possible.

However, note that this is still a self-study course for the most part.

I won’t be able to guarantee detailed 1-on-1 support to everybody due to the large number of students taking the course, but I’ll still try to answer any questions you may have to the best of my ability.

Yes! If you’re a student, this course will also work as an excellent complementary resource for courses on Lagrangian mechanics, theoretical mechanics, classical field theory or quantum field theory.

However, do note that this isn’t meant as an academic resource and this course has no affiliation to any university, so there are no grades, exams or credits associated with this course.

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!

sign me up!