Analytical Definition and 280 Threads

TL;DR Summary: analytical mechanics ressources Pleaaaaaaase , can someone send me ressources to study analytical mechanics ...??? I'm hopeless

For a while I've been trying to get a better understanding of how Descartes' invention of Cartesian space revolutionized math. It seems like an invention on par with the invention of agriculture in how it led to human progress. I am still having trouble, though, pinpointing examples of what can...

Hi, I'm working on a simple FEA involving a preloaded bolt: The bolt is modeled as a single part (shank + head + nut), glued (perfect bonding) to both rings. Pretension force ##F_{preload}=200 \ N## is applied in the first step of the analysis while in the second, pretension force stops...

Hello everyone, I'm trying to solve the transient heat transfer problem within the ID wall. The material is steel, and it is isotropic. The properties are given below : L = 5 mm qin = 0 Tinf = 100 deg C Tini = 20 deg C rho = 7850 kg/m3 cp = 460 W/Kg.K k = 45.8 W/m.K h = 20 W/m^2.K alpha = k /...

Hi. If I turn on an antenna, it starts sending out radiation. If I turn it off again, the radiation doesn't instantly disappear but dies out smoothly (exponentially?). But this also means the radiation is never completely gone. This looks time-asymmetric, which is weird for electrodynamics. It...

Is there analytical proof that a photon Pe will be emitted by an excited atom Ae when another photon Pp of the same frequency is passing by Ae in LASER production? I tried using Feynman diagram to show a high probability of this event. I failed (most likely because I am not an expert in QFT)...

I have a equation with a double sum. However, one of the variables in one of the sums comes from a stochastic distribution (Gaussian to be specific). How can I get a closed form equivalent of this expression? The U and Tare constants in the equation. $$ \sum_{k = 0}^{N_k-1} \bigg [ \big[...

So I was looking at this example problem in my textbook and I don’t understand how they got -168.1 degrees. The part I’m confused with is the first part of the 2nd picture, there’s a coma in the inverse tan, I don’t know what that means.

Hi, I have recently become interested in analytical solutions of various advanced solid mechanics problems, mostly nonlinear ones. I consider simple geometries and loads (like bending of beams, torsion of shafts, or internal pressure in pipes), but for nonlinear materials. I have learned that...

Hi, I am trying to find open-form solutions to the integrals attached below. Lambda and Eta are positive, known constants, smaller than 10 (if it helps). I would appreciate any help! Thank you!

Hi all, Currently I am working on a home-project, making a trike. Now just for fun and because I like to calculate things, I calculated the deflection of a frame with a load. The frame is shown in the picture below, I added the force for clarity. With my analytical calculation I found a...

A 4×3 matrix which has all elements empty, now I select any two consecutive elements until all elements are selected. I assign an index number (1 to 12) to the matrix element, in one row there are only 1,2,3 elements and 3 & 4 are not consecutive. for example, if I select index 1 & 2 of the...

I have a Gaussian shape frequency domain spectrum of which I am calculating the Inverse Fourier transform. I use both IFFT of MATLAB and also an analytical expression of Mathematica. They are not the same. I don't know where it is wrong. I have pasted both the figures. The numerical one has...

I have an expression of Matter Angular power spectrum which can be computed numerically by a simple rectangular integration method (see below). I make appear in this expression the spectroscopic bias ##b_{s p}^{2}## and the Cosmic variance ##N^{C}##. ## \begin{aligned}...

Can a point P on the smaller wheel trace a straight line path inside the circular road (like the walls of a well)

Hi, one of the most interesting experimental tests performed for rotating machinery (such as gas turbines) is blade containment test - if the blade detaches from the hub, it can't break through the cover of the turbine because it could result in catastrophic damage (especially in case of...

The freefall wiki entry wiki Freefall has an analytic solution for freefall distance in a gravitational field, but ... it doesn't seem to work ... at least i can't get it to work ... here is my MATLAB program to test it ... clear G=6.7e-11; % gravitational constant m^3/(kg*s^2) mEarth =...

Hi guys, I managed to solve this problem just by "rewriting" the first equation of the system as ##t=f(x)## and then substituting that in the second ##y=f(t)## equation, ending(of course) up with the sought ##f(x,y)## function. The problem here is I didn't really understand what I have done and...

Why, in lagrangian mechanics, do we calculate: ##\frac{d}{dt}\frac{\partial T}{\partial \dot{q}}## to get the (generalised) momentum change in time instead of ##\frac{d T}{dq}##? (T - kinetic energy; q - generalised coordinate; p - generalised momentum; for simplicity I assumed that no external...

Hi, I came across some interesting frames recently. Here they are: I wonder if all these frames can be solved analytically. If yes then how to do it ? Examples a) and d) are planar frames with diagonal members while b) and c) are spatial frames: b is subjected to uniformly distributed load...

Hi, I ran into problems using the poisson ratio. For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge. Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir. The material parameters are E = 100, and v...

So I am working on a project where I have a tank, which has a volume of electrolyte liquid inside it. This is coupled to a battery which charges it, and gives it energy. I will have a copperband arround it, so i can measure a potential voltage from the electrical field. So what I need to...

Hi, In my course in analytical mechanics, it is said that for a system of n particles subjected to r constraint equations, it is necessary to impose regularity conditions on the constraint surface defined by G = 0 where G is a function of the position of the position of the particles and time...

Hi, I have a question regarding plastic bending of beams (assuming bilinear elastoplastic material - with or without hardening) . In literature one can find calculations of load capacity for those beams. But what else can be calculated in such case ? Stresses ? Deflection ? Where can I find...

Does anyone know if it is possible to develop a fully analytical solution for a leaky integrate and fire neuron driven by arbitrary time-varying current? Here's what I have so far (setting as many possible constants to 0 and 1): The equations: ## \dot{V} = - V + I(t) ## and if ##V(t) = 1##...

This is my problem : it all starts with some very basic linear least-square to find a single parameter 'b' : Y = b X + e where X,Y are observations and 'e' is a mean-zero error term. I use it, i find 'b', done. But I need also to calculate uncertainties on 'b'. The so-called "model uncertainty"...

Is this anyhow possible ? The system would be a wave equation modelized by a finite elements basis in space and time. Is there any method to do the limit discretization->continuum with paper and pencil ?

In a numerical Fourier transform, we find the frequency that maximizes the value of the Fourier transform. However, let us consider an analytical Fourier transform, of ##\sin\Omega t##. It's Fourier transform is given by $$-i\pi\delta(\Omega-\omega)+i\pi\delta(\omega+\Omega)$$ Normally, to find...

As you can see from the very last line of my post, this whole post may come from the fact that I don't get sarcasm o0)Hi, reading the above mentioned book I ran into the following footnote: Postulate A was earlier stated as: An alternative, but equal, version of Postulate A is given the page...

When considering the forward FFT of a mathematical function sampled at times ##t = 0, \Delta, \ldots, (N-1) \Delta##, following the usual convention, we have something like $$ H(f) = \int_{-\infty}^{+\infty} h(t) e^{-2 \pi i f t} dt \quad \Rightarrow \quad H_k = \sum_{n=0}^{N-1} h_n e^{-2 \pi i...

Hello my dear physicists, I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...

So I've derived the rocket equation in empty space and with constant gravity. Now I am interested in adding air resistance. I'm aware that there are 2 different models as if 0<Re<1 then F_drag=k*v and if 1000<Re<30000 then F_drag=1/2*A*rho*CD*v^2. And for my purpose the second model is most...

I mean I know they are linear since they obey the ohms law. But I don't quite understand the reasoning that since, say, V=Ldi/dt and taking a derivative is a linear operation therefore it is a linear device?? I can verify that sin'(x) = cos(x) or sin(x+90) so the signal is time shifted but...

Consider the mono-group model and a ramp in reactivity like ##\rho = -\gamma \beta t## The system is $$\frac {dP}{dt} = \frac {\rho - \beta}{\Lambda} P + \lambda C$$ $$ \frac {dC}{dt} = \frac {\beta}{\Lambda} P - \lambda C$$ 1st method: assume that the concentration of precursor doesn't...

Hi All, I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.I've already found information involving a rectangular flow...

Homework Statement Hello, I am currently working on photon diffusion equation and trying to do it without using Monte Carlo technique. Homework Equations Starting equation integrated over t: int(c*exp(-r^2/(4*D*c*t)-a*c*t)/(4*Pi*D*c*t)^(3/2), t = 0 .. infinity) (1) Result...

I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...

I have an equation regarding integration equation. Given: where is found analytically to be: My question is what is the analytical equation for equation 3? I hope that anyone may help me regarding this matter. This is the paper I referred: https://arxiv.org/pdf/1503.05793.pdf Thank you.

Sometimes there are functions that are initially defined for only integer values of the argument, but can be extended to functions of real variable by some obvious way. An example of this is the factorial ##n!## which is extended to a gamma function by a convenient integral definition. So, if I...

First time in this forum, so greetings to everyone! I am currently working with some physical models in the field of natural ventilation and I came across the following 5th order polynomial equation (quintic function): $X^{5}+ C X - C =0$ This is the steady state solution of a physical system...

The analytical solutions are: \begin{equation} \psi(x) = \begin{cases} Ce^{\alpha x}, \text{if } x < -\frac{L}{2}\\ Asin(kx) + Bcos(kx), \text{if } -\frac{L}{2} \leq x \leq \frac{L}{2}\\ Fe^{-\alpha x} , \text{if } x > \frac{L}{2} \end{cases} \end{equation}...

Let's consider a particle moving along x – axis, its position at t = 1s is 1m and speed is 1 m/s. How can one calculate acceleration on the basis of this information?

I know I can't speak for everyone here, but I would presume that most people in the sciences have either naturally or through schooling become analytical thinkers. Especially for the ones that are naturally analytical, have you found difficulty in being spontaneous, romantic, artistic, or any...

Hi at all. I'm wondered is necessary learn well analytical mechanic ( eg learning The Goldstein's book), for understand and study QM ?

Greg Bernhardt submitted a new PF Insights post The Homopolar Generator: An Analytical Example Continue reading the Original PF Insights Post.

I am trying to write code for analytical solution of 1D heat conduction equation in semi-infinite rod. The analytical solution is given by Carslaw and Jaeger 1959 (p305) as $$ h(x,t) = \Delta H .erfc( \frac{x}{2 \sqrt[]{vt} } ) $$ where x is distance, v is diffusivity (material property) and t...

The pioneering work by G. Lehmann, M. Taut, please see the attached files or download from wiley On the Numerical Calculation of the Density of States and Related Properties, http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220540211/abstract The question is how the middle line of Eq. (3.9)...

Hi at all. According to you which of the two texts, between Landau-Lifshitz (mechanics) and the Goldberg (classical mech) is better for study Analytical Mech ? Or there are other better ones ?

Hello, I need to find the matrix elements of in the particular case where l = 1. This should have an analytical solution but I have no idea where to start with this demonstration. Any suggestions on where to start digging?Ty!

Is it possible to integrate the following function analytically? ##\int_{0}^{\infty} \frac{\exp{-(\frac{A}{\tau}+B\tau+\frac{A}{\beta-\tau})}}{\sqrt{\tau(\beta-\tau)}}d\tau,## where ##A##, ##B## and ##\beta## are real numbers. What sort of coordinate transformation makes the integral bounded...