Theoretical mechanics Definition and 22 Threads

I remember one of the Ant-Man movies had time travel enabled by shrinking down to an incredibly small size. This seemed silly to me at first but then I realized that a second is much closer to the age of the universe than a Planck time is to a second. This is mind-boggling and the human brain...

I took the derviative of the Hamiltonian function with respect to Q and assumed that it was equal to 0 in order to find the Konstant A. I did find the Konstant A as -1/2m^2g but I still cant write the Hamiltonian equation without having the Q as a variable. Can someone please help? Translation...

Two point-like particles of mass m. The particles are rigidly connected to each other with a mass-less rod of length L. The particles are initially at rest in such a way that one particle is at the origin and the other is at the point (0, L). A point-like particle of mass M collides with a...

A rough explanation of my attempts: I set the coordinate axis in a way that x is the horizontal base and y is perpendicular. But I guess it is a 3d problem, so I struggle finding the right position of the coordinate system. Then, my next step was applying 2nd NL for every axis. So far I have...

With the Liouville's theorem $$\frac{{d\rho }}{{dt}} = \frac{{\partial \rho }}{{\partial t}} + \sum\limits_{a = 1}^{3N} {(\frac{{\partial \rho }}{{\partial {p_a}}}\frac{{d{p_a}}}{{dt}} + \frac{{\partial \rho }}{{\partial {q_a}}}\frac{{d{q_a}}}{{dt}})} = 0$$ when we calculate the time evolution...

Summary: Mechanics problem related with Calculus (differential equations) Hi everyone, I would like some help in that task, if anyone would be willing to help :) Namely I have a problem from particle dynamics. "D:" means given info... so, D: m,g,h,b, miu. We're looking for v0 and S as given...

The building of theoretical mechanics can be constructed using only the first and the second derivatives (those of coordinates in case of kinematics: velocity and acceleration and those of energy in case of dynamics: force and gradient thereof). It is obviously unavoidable if one wants to deal...

Hello. I have some problems with making Lagrangian. I need your advice. 1. Homework Statement I have this situation: Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ. Homework Equations [/B] L = U - V The Attempt at a...

Homework Statement [/B] Here's the problem from the homework. I've called the initial positions in order as 0, l, and 2l. Homework Equations The most important equation here would have to be |V - w2*M| = 0, where V is the matrix detailing the potential of the system and M as the "masses" of...

Homework Statement Dear All, I'm having a hard time solving the following problem: A point of mass is moving on a circular plane (Oxy), where the circle's formula is: The force acting on mass "m" is defined as: We're looking for velocity of point "m" in position (1,1) =V1, and in position...

Classical mechanics: a minimal standard course by Sergei Winitzki. It is not probably going to help you if you already did not know the subject but is a great refresher nonetheless. He also includes a differential equations refresher that I found invaluable. Looks like he has a ton of other...

I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite...

I'm trying to determine how exactly gear ratio limits velocity. I know that a high torque configuration is generally regarded as low speed, but my calculations do not seem to support that. Basically, I've written a small problem where we have an input gear with constant torque and an output...

Homework Statement [/B] A low flying Earth satellite travels at about 8000m/s. For the satellite, the relativistic factor $$\gamma = \frac{1}{\sqrt{1-\beta^2}}$$ where $$\beta = \frac{v}{c}$$ is close to 1 because v<<c. Estimate by how much gamma actually deviates from 1 by expanding gamma in...

Homework Statement Homework EquationsThe Attempt at a Solution See LaTeX[/B] given that $$v^2 = v_o^2 + \frac{2}{m}\int\limits_{x_o}^x F(x) \ dx\ $$ find the speed v(t) and the position x(t) given that $$F = F_o$$ and $$v(t=0)=0$$. I tried plugging in $$F=F_o$$ for $$F(x)$$ in the above...

I'm new to this site, so please bear with me. 1. Homework Statement A particle of mass m has speed v(x) = α/√x. Calculate the force F(x) responsible. Then, calculate the displacement x(t) of the particle. Homework Equations [/B] The equations that I believe we are supposed to use are f=ma...

I know Single variable Calculus and I have a basic understanding of multivariable calculus. I also happen to know basic linear algebra. What are the mathematical pre-requisites needed in order to self-study theoretical mechanics? I'm planning to take this course...

Suppose I come up with a system that has certain number of particles with certain masses and are interconnected between each other in a certain way and are acted by forces which are also part of the system. What's the general rule for finding potential and kinetic energies as functions of...

Homework Statement A projectile is launched horizontally. A retarding force acts on the projectile of the form F = -Ae^(cv). Find it's speed as function of time. Homework Equations F = ma The Attempt at a Solution m(dv/dt) = -Ae^(cv) e^(-cv) dv = (-A/m) dt I integrated the...

Author: Alexander L. Fetter Title: Theoretical Mechanics of Particles and Continua Amazon Link: https://www.amazon.com/dp/0486432610/?tag=pfamazon01-20

Here's a simple question. Anyone who knows the answer can save me from some effort by telling the answer. For arbitrary canonical transform (q,p)\mapsto (Q,P) in the Hamilton's formulation, does there always exist a corresponding transformation q\mapsto Q in the Lagrange's formulation? By...

So I'm stuck on the second part of this problem and really don't know hwere to go from here... let me type it up and show where I got stuck at. 3. The motion of particle of chage q in an electromagnetic field is governed by the Lorentz force (for low velocities v<<c): F=qE + qvxB. With both...