# What is Landau and lifshitz: Definition and 26 Discussions

In physics, the Landau–Lifshitz–Gilbert equation, named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the precessional motion of magnetization M in a solid. It is a modification by Gilbert of the original equation of Landau and Lifshitz.
The various forms of the equation are commonly used in micromagnetics to model the effects of a magnetic field on ferromagnetic materials. In particular it can be used to model the time domain behavior of magnetic elements due to a magnetic field. An additional term was added to the equation to describe the effect of spin polarized current on magnets.

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1. ### Conservation of the Laplace-Runge-Lenz vector in a Central Field

I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...
2. ### I Trouble simplifying the Lagrangian

Hello, I have posted a similar thread on this question before, but I'd like to get some help to simplify the answers I've got so far in order to match the solutions provided. If anyone could help me, I would really appreciate it. Since (c) is quite similar to (b), I'll leave here what I've done...
3. ### I Trouble understanding coordinates for the Lagrangian

Hello, I'm having some trouble understanding this solution provided in Landau's book on mechanics. I'd like to understand how they arrived at the infinitesimal displacement for the particles m1. I appreciate any kind of help regarding this problem, thank you!
4. ### I Understanding the Coordinates in the Lagrangian for a Pendulum

So I've been studying classical mechanics and have come across a small doubt with the solution provided to the problem in question from Landau's book. My question is: why are the coordinates for the particle given as they are in the solution? I imagine it has something to do with the harmonic...
5. ### Perturbation theory and the secualr equation for double degeneration

I've been assigned to do a problem from Landau which you can read below: I have no problem with finding the energy. Then I write down the equations: \begin{equation*} \begin{cases} (V_{11}-E^{(1)})|c_1|e^{i\alpha_1} + V_{21}e^{i\alpha_2}|c_2| = 0\\ V_{12}e^{i\alpha_1}|c_1| +...
6. ### Landau vol.1 Mechanics: Expansion of L' and Dependence on Velocity

Let ##K## and ##K'## be two inertial frame, If K is moving with infinitesimal velocity relative to ##K'## , then ##v' = v + \epsilon##. Note that ##L(v^2) - L(v'^2)## is only a total derivative of a function of coordinate and time. (I understand this part) Because ##L' = L(v'^2) = L(v^2 +...
7. ### Other Math required for advanced classical mechanics

What types of math should a student be comfortable with going into a classical mechanics class at the level of Landau and Lifshitz? And are there any additional types of math that aren’t required, per se, but would be beneficial to know (for said course)?
8. ### Classical Classical Mechanics: Landau vs Goldstein Textbooks

Which textbook is better for an upper division course in classical mechanics - Goldstein’s book or L&L’s book?
9. ### I How Is Particle Distribution in a Solid Angle Derived in Mechanics?

I'm reading Mechanics by Landau and Lifshitz, chapter IV, and trying to understand how in a (closed) center of mass system, with randomly distributed and oriented particles that disintegrate, "the fraction of particles entering a solid angle element ##do_{0}## is proportional to ##do_{0}##, i.e...
10. ### I Varying The Relativistic Action

In his book, Landau mentioned varying the relativistic lagrangian However, I do not understand how he got from varying the integral of ds to varying only the contravariant components. Would the general procedure not be varying $$\delta S = -mc\delta\int_a^b\frac{dx_idx^i}{\sqrt{ds}}$$ and...
11. R

### A The Lagrangian a function of 'v' only and proving v is constant

Hi everyone. So I'm going through Landau/Lifshitz book on Mechanics and I read through a topic on inertial frames. So, because we are in an inertial frame, the Lagrangian ends up only being a function of the magnitude of the velocity only (v2) Now my question to you is, how does one prove that...
12. ### Lagrangian and Slonczewski-like torque

To include slonczewski-like torque in the Lagrangian there enter as dissipation by Rayleig function? ST= σ m x (m x mp) where m is the magnetization in free layer and mp current direction in the pinned layer (-z). The Rayleig function is: RF=(dm/dt+σ m x mp)2 Then L= ∫ (RF+E)dx Thanks
13. ### Meaning of trajectory in four-electricity in Landau's book

Homework Statement I think the in equation ##(28.2)##,##x^i## in ##\frac{dx^i}{dt}## and the ##x^i## decides ##\rho## is not the same,if they are equaivalent,##\rho## can not vary with position changing and time fixed, because ##\frac{dx^i}{dt}## indicate the ##x^i(t)## which means if position...
14. ### Spherical Pendulum - elliptic integral

Hello everyone. In the 3rd edition of Mechanics by Landau and Lifshitz, paragraph 14, there is a problem concerning spherical pendulum. Calculations leading to the integral $$t=\int \frac {d \Theta} {\sqrt{\frac{2}{ml^2}[E-U_{ef}(\Theta)]}},$$ ...
15. ### Nonholonomic mechanics in Landau and Lifshitz

<<Mentor's note: this is spin-off this thread>> One error I'm aware of in LL vol. I is the claim on integrability. But what's wrong with LL's treatment of anholonomous constraints (in sectin 38 in my German edition)? It just leads to the usual equations with Lagrange parameters you also get...
16. ### Forced oscillations and resonance (bis)

I'm studying from landau lifšits "mechanics". I had some troubles in section small oscillations-->forced oscillations, especially from eq 22.4 to eq 22.5 i searched the web and came across this: https://www.physicsforums.com/threads/forced-oscillations-and-ressonance.488538/#post-3236442 this...
17. ### Derivation from Landau and Liffshitz, vol 6

I have starting working through section 134 of Landau and Lifshitz, vol 6, and it seems I have entered some kind of twilight zone where all my math/physics skills have left me :cry: The derivation starts with the energy-momentum tensor for an ideal fluid: ## T^{ik} = wu^i u^k - p g^{ik} ##...
18. ### Course of Theoretical Physics by Landau and Lifshitz

Author: L.D. Landau, E.M Lifshitz Title: Course of Theoretical Physics Amazon Link: https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20 https://www.amazon.com/dp/0750627689/?tag=pfamazon01-20 https://www.amazon.com/dp/0750635398/?tag=pfamazon01-20...
19. ### What level are Landau and Lifgarbagez books suitable for?

Is Landu & his student Lifgarbagez's all book really for a good read.Also can you give me details about the Level of Book Undergraduate or Graduate.
20. ### How to get this equation - Mechanics by Landau and Lifshitz

In page 28 of Mechanics by Landau and Lifgarbagez, there is the following equation. \int_0^\alpha \frac{T(E) dE}{\sqrt{\alpha-E}}=\sqrt{2m}\int_0^\alpha \int_0^E \left[ \frac{dx_2}{dU}-\frac{dx_1}{dU}\right] \frac{dU dE}{\sqrt{[(\alpha-E)(E-U)]}} Then, by changing the order of integration...
21. ### Question on Landau and Lifshitz volumes

What are the mathematical prerequisites of these books? In particular, what are the mathematical prerequisites of volume I?
22. ### Landau and Lifshitz Course - any particular order?

Hi everyone, I'm currently working through volume 1 - mechanics. I'm planning on doing the whole series over the course of the next few years, but there are a few topics I'd like to get to before others. I was just wondering if they are meant to be read one after the other, or if they were...
23. ### Solving the Mystery of "spe******ts

"Landau and Lifshitz" I was reading some other forum when I found word "spe******ts" - it took me some time to understand what I am seeing. Perhaps I should post it in brain teasers :smile:
24. ### Covariant divergence question from Landau and Lifshitz

Hi everyone, I'm trying to work through section 86 of Landau and Lifgarbagez volume 2 (The Classical Theory of Fields). Basically, I am unable to get equation (86.6) from equations (86.4) and (86.5). I've detailed my working/question in the attached jpg file. I would appreciate any inputs...
25. ### Classical theory of fields by landau and lifshitz

is this book good for studying e&m and general relativity?
26. ### I'm having major problems with Landau and Lifshitz Mechanics

i'm having major problems with mecanics because the recomended textbook mechanics by landau and lif****z is far too mathematical. can anyone recommend a book which covers similar material with less general equations etc? I'm willing to lower myself to using engineering books!