Classical mechanics Definition and 1000 Threads

Suppose we have mass ##m## attached to spring with constant ##k##, and some coefficient of kinetic friction ##\mu## between the mass and the surface. Its displaced from equilibrium by some distance ##x## at ## t = 0 ##. I've come up with the following ODE to described ##x(t)## using the...

Consider the following setup where the bead can glide along the rod without friction, and the rod rotates with a constant angular velocity ##\omega##, and we want to find the constraint force using Lagrange multipliers. I chose the generalized coordinates ##q=\{r,\varphi\}## and the...

I'm just getting started on Lagrangian mechanics and what I can't understand is, how did Lagrange discover the Lagrangian? Did he just randomly decide to see what would happen if we calculate KE - PE or T - V and then discovered that the quantity is actually mathematically and physically...

My question is about the general relationship between the constraint functions and the constraint forces, but I found it easier to explain my problem over the example of a double pendulum: Consider a double pendulum with the generalized coordinates ##q=\{l_1,\theta_1,l_2,\theta_2\}##,: The...

For a rigid body with three principal axis with distinct moments of inertia, would the principal axis with the intermediate moment of inertia still be unstable in ideal conditions, e.g. no gravity, no friction etc.? From the mathematical derivation I deduce that it should be unstable, since we...

I learned some computer science basics from the book SICP ( Structure and Interpretation of Computer Programs, Authors: Gerald Jay Sussman, Hal Abelson, Julie Sussman ) and I've witnessed a book about mechanics from the same author called Structure and Interpretation of Classical Mechanics...

In classical mechanics, it seems like solving force equations are a question of finding a solvable system of equations that accounts for all existing forces and masses in question. Therefore, I'm curious if this can be mixed with reinforcement learning to create a game and reward function...

The invariance of this volume element is shown by writing the infinitesimal volume elements $$d\eta$$ and $$d\rho$$ $$d\eta=dq_1.....dq_ndp_1......dp_n$$ $$d\rho=dQ_1.......dQ_ndP_1....dP_n$$ and we know that both of them are related to each other by the absolute value of the determinant of...

The homework statement isn't exactly as is mentioned above. The actual problem statement is as follows: This is problem 3.8 from John R. Taylor's Classical Mechanics; however, my question is not related to the main problem itself but one particular aspect of it. Now, in the same textbook (John...

Goldstein's Classical Mechanics makes the claim (pages 382 to 383) that given coordinates ##q,p##, Hamiltonian ##H##, and new coordinates ##Q(q,p),P(q,p)##, there exists a transformed Hamiltonian ##K## such that ##\dot Q_i = \frac{\partial K}{ \partial P_i}## and ##\dot P_i = -\frac{\partial...

I think product of inertia always zero because rolling motion of disk is fully balanced

I am attempting problem number 2.38 from John R. Taylor's Classical Mechanics and I am not getting the correct answer. My procedure is as follows: Equation of motion (taking up as the positive direction): $$m\dot{v}=-mg-cv^2$$ Now to find ##v_\mathrm{ter}##, the terminal velocity, we consider...

I am self studying Goldstein first chapter "A survey on the elementary principles", so far I have been enjoying it, sometimes he skips some lines while deriving a principle or so, therefore sometimes I get to PSE or Physics Forums to know the things I lack understanding in. What are your...

I am intending to join an undergrad course in physics(actually it is an integrated masters course equivalent to bs+ms) in 1-1.5 months. The thing is, in order to take a dive into more advanced stuff during my course, I am currently studying some of the stuff that will be taught in the first...

I plan to add on to this as I have time and ability. Apologies for the weird formatting.

We have 2 objects, m1 and m[SUPlB]2[/SUB] Friction is present between the two objects but not between m1 and the floor. A force is exerted on the bottom object which causes it to accelerate parallel to the floor. The thing I'm wondering for while now is, how do I prove that the acceleration of...

From a classical mechanics perspective I understand the force interactions leading to the phenomenon, but from a matter perspective, what is a "positive" or "negative ly" charged water stream? Is this referring to the spontaneousH(+) + OH(- )formations?

I just calculated the Lagrangian of a particle of mass ##m## in a radially symmetric potential ##V(r)##. I thought it would be a good idea to switch to spherical coordinates for that matter. What I get is $$ L = \frac{1}{2} m \left( \dot{r}^2 + r^2 \dot{\theta}^2 + r^2 \dot{\varphi}^2...

I have been trying to understand this proof from the book 'Introduction to classical mechanics' by David Morin. This proof comes up in the first chapter of statics and is a proof for the definition of torque. I don't understand why the assumption taken in the beginning of the proof is...

I have attempted but with no result.

I tried writing this out but I think there is a bug or something as its not always displaying the latex, so sorry for the image. I have gone through various sources and it seems that the reason for u being small varies. Sometimes it is needed because of the taylor expansion, this time (below) is...

Necessary condition for a curve to provide a weak extremum. Let ##x(t)## be the extremum curve. Let ##x=x(t,u) = x(t) + u\eta(t)## be the curve with variation in the neighbourhood of ##(\varepsilon,\varepsilon')##. Let $$I(u) = \int^b_aL(t,x(t,u),\dot{x}(t,u))dt = \int^b_aL(t,x(t) +...

My issue is in deriving the coordinates of a point on a wheel that rotates without slipping. In Morin's solution he says that: My attempt at rederiving his equation: I do not understand how the triangle on the bottom with sides indicated in green is the same as the triangle on top that is...

I was taking notes from a lecture on Quantum Physics and during the introduction, they gave an example of what led to the discovery of Quantum Physics: The electric bulb example where the brightness and colour of light depended on the temperature of the filament(see...

The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...

I was reading the oscillations chapter which was talking about how to solve linear differential equations. He was talking about how to solve the second order differential below, where a is a constant: In the textbook, he solved it using the method of substitution i.e guessing the solution...

[This is a continuation of OP's thread here: https://www.physicsforums.com/threads/satellite-mechanics-linear-and-rotational-momentum.1046963/ ] satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a...

I think that yes but how to explain it when someone standing on a ground sees them moving paralell? If I move properly, I can see two cars moving paralell ralative to the ground crashing, while someone on the ground do not see them crashing. Is it consistent?

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...

satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a squared satellite weighting 100kg, 1 meter on each side. it has a thruster on it's side, shown in picture thruster quickly ejects 100g of propellant...

Mcauley's "Classical mechanics: transformations, flows, integrable and chaotic dynamics" has a very interesting table of contents, and it has a philosophy of approaching Hamiltonian flows and chaos without using the formalism of modern differential geometry. Unfortunately, after reading the...

TL;DR Summary: Distance traveled by a car considering only air friction? How much distance would a 3-ton car travel if its initial speed was 17 km/h and we only take into account air's friction? (Assume that the car has an airfoil-like shape, so that the resistance against the air is very low)...

My Progress: I tried to perform the coordinate transformation by considering a general function ##f(\mathbf{k},\omega,\mathbf{R},T)## and see how its derivatives with respect all variable ##(\mathbf{k},\omega,\mathbf{R},T)## change: $$ \frac{\partial}{\partial\omega} f =...

Hello, Has anyone read/heard about the textbook Variational Principles in Classical Mechanics, written by Douglas Cline? Any thoughts on whether I could use it as a replacement for Goldstein? Thank you!

I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...

"Reversibility means that we never lose information, that at a fundamental level we can always retrodict the past as well as predict the future in the laws of physics". Susskind in his Theoretical minimum Lecture 2 describes about the laws which are true and which are not. He tells the law of...

Summary: The initial problem states: Consider a free particle of mass m moving in one space dimension with velocity v0. Its starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1 at time t = t1 > 0. and this info is to do the 3 problems written out. a)...

beyond 1.) the Newtonian formulation 2.) The lagrangian formulation 3.) The Hamiltonian formulation What other formulations are there

Imagine we attach an imaginary cosmological scale rope to an object that is very far away from us. Before attaching the string, the object would be receding from us due to spacetime expansion. After attaching it, tension would form in the string and we would eventually stop the object. After...

The result I get is 2 hours and 10 minutes. My reasoning is down here. But! Checking the map for the 2024 Solar eclipse, https://www.timeanddate.com/eclipse/map/2024-april-8, in many locations you can see a partial eclipse of over 2 hours 40 minutes. What is the main source of error here? Here...

I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α) And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.

I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.

Inside the textbook, the prerequisites state first year mechanics and some differential equations, although it continues to say the differential equations can be learned as you’re working your way through the book, as differential equations were basically “invented” to be used for applied...

Seven years ago, I wanted to share and discuss my experiments results there but it was not possible since there was no published peer review paper yet and apparently not fulfilling forum requirements. Now we have such a publication, but still not sure the subject can be discussed here. Anyway...

I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an...

Its clear in elastic collision that both KE and momentum is conserved. Bodies exchange their velocities. It is seen clearly in this video. There is no decrease in speed. Total KE is constant. But in an inelastic collision momentum is conserved again but not the KE. There is loss in KE (I guess...

[Mentor Note -- thread moved from the schoolwork forums to GD as it seems like a more general question] Homework Statement:: Topoisomerases help in relieving strain in the DNA ahead of the replication fork caused by the untwisting of the double helix (Topoisomerases are enzymes that...

I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below

Hi, A body with center of mass behaves as a point mass when a force is applied. So when ##F_{ext}=0## then does it also behave as a point mass with ##a_{com}=0##, at rest. If yes, How can we prove this? (And can somebody please answer my other question I posted a week ago...

https://www.physicsforums.com/threads/conservation-of-momentum-and-loss-of-energy-in-inelastic-collisions.311037/post-2182192 If I understand correctly mathematically the momentum of the system remains unchanged but individual momentums decreases always. In an inelastic collision the momentum...