Derivation Definition and 1000 Threads

Let me show you part of a book "Mechanics From Newton’s Laws to Deterministic Chaos" by Florian Scheck. I do not understand why these integrands can differ by more than time derivative of some function M. Why doesn't it change the value of integrals? It seems this point is crucial for me to...

I'm working through Gregory's Classical Mechanics and came across his derivation of energy conservation for a system of N particles that is unconstrained. We get to assume all the external forces are conservative, so we can write them as the gradient of a potential energy. There's a step he...

Homework Statement Is it possible to accurately approximate the speed of a passing car while standing in the protected front hall of the school? Task: Determine how fast cars are passing the front of the school. You may only go outside to measure the distance from where you are standing to the...

Hello, I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for...

Homework Statement My question here isn't a specific question that has been given for homework, but a more general one. For an assignment I have to 'derive an expression for the resonant frequency, ω0' for two different systems, the first for 'a mass M connected to rigid walls via two springs'...

Homework Statement I don't understand the derivation of the right side of the last equation. Homework EquationsThe Attempt at a Solution I got to this point, I also don't understand why it did not include C_2 for the variation of temp. along the fin. I am guessing the right side is the...

Riemann tensor is defined mathematically like this: ##∇_k∇_jv_i-∇_j∇_kv_i={R^l}_{ijk}v_l## Using covariant derivative formula for covariant tensors and covariant vectors. which are ##∇_av_b=∂_av_b-{Γ^c}_{ab}v_c## ##∇_aT_{bc}=∂_av_{bc}-{Γ^d}_{ac}v_{db}-{Γ^d}_{ab}v_{dc} ##, I got these...

Self-repost from physics.SE; I underestimated how dead it was. So this follows Schroeder's Intro to Thermal Physics equations 6.1-6.7, but the question isn't book specific. Please let me be clear: I know for a fact I'm wrong. However, it feels like performing seemingly allowed manipulations, I...

In the derivation of F=ma, when we reach the point F=kma, we take k=1. Why can't we take 'k' as some other value? I will be thankful for help!

So this should be coming easily, but for some reason I can't seem to grasp why or how this is being done: So say we have equation: 0 = a + (μ/r3) r , where μ = G(M+m) or ≈ GM and M >> m. According to this book, the first step to finding ξ, the Specific Mechanical/Orbital Energy they dot...

When reading a textbook I came across some reasoning about Schrödinger Equation. It started with the wave function $$\nabla^2\psi=k^2\psi$$ I am a bit lost at this point. Where does the right side of the equation come from? What should I review to fix that part of my knowledge?

Homework Statement I really don't know if I'm in the right subforum... I've started reading this text on statistical mechanics from MIT, but I'm stuck on page 2. Here's the statement: Let the equilibrium state of systems A, B, and C be described by the coordinates {A1, A2,· · ·}, {B1, B2,·...

Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...

I really love seeing derivations of the EFE's, Maxwell's equations, Schrodinger equation etc. I have seen a number of derivations of Maxwell's Equations but this is the shortest, most illuminating and best I have come across - it basically just uses covarience - and as it says - a little bit...

Hello, I have seen that biot savart's law works for infinitely narrow wires: "The formulations given above work well when the current can be approximated as running through an infinitely-narrow wire." When I wanted to derive the magnetic field of a solenoid, I had to do this substitution...

I am trying to see how to derive the following inequality on page 36 in the proof of Lemma 11.3: https://arxiv.org/pdf/math/0412040.pdf I.e, of: $$\| fg \|_{Lip} \le \bigg(1+\ell \sup_{t\in T} |g'(t)|\bigg)\sup_{t\in T}|f'(t)| , \ \ supp \ f(1-g)\subset S^c$$ My thoughts about how to show...

Hi, Page 166, theorem expressed as 7.2, does anybody know it's name? Many thanks

I don't understand the reasoning for any of the three constraints imposed. why would ##dtdx^i## terms indicate a preferred direction? what if there was identical terms for each ##x^i## would there still be a specified or preferred direction? (or is it that in this case we could rename ##t## to...

I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help. My doubt ELI5...

Hi, I came across a derivation notation I didn't recognize: Let ##s## be some four-vector and ##\tau## the proper time. What is the significance of $$\frac{Ds}{\mathrm{d}\tau}?$$ I know ##Ds## can be used to mean the Jacobian, but I've never come across the notation above. Does someone...

Related to Figure 8.4 the author mentions this when stating (8.25): "Note that the semi-circle deviates below the real -axis, rather than above, because the integral is calculated by letting the pole approach the axis from the upper half-plane in -space." Why is the pole calculated in this way...

The question: Show that the Lorentz condition ∂µAµ =0 is expressed as d∗ A =0. Where A is the four-potential and * is the Hodge star, d is the exterior differentiation. In four-dimensional space, we know that the Hodge star of one-forms are the followings. 3. My attempt Since the four...

Hi all, I understand where Archimedes' Principle comes from in liquids: If we imagine a cylinder immersed in a liquid of density ρ whose cross-sectional area is A and whose top is at depth h1 and whose bottom is at depth h2: Force(top of cylinder) FT = ρgh1A Force(bottom of cylinder) FB =...

I think that dU = Cv dT can only be used when the volume of the gas is constant. Similarly, Cp = dQ/dT can only be used when the pressure is constant. Such as We have Cv=dQ/dT and ΔU=Q+W dU=Q+pdV Therefore, dU/dT = dQ/dT only when dV is zero Why am I wrong? Thank you so much for your help. The...

On page 208 of Ashcroft and Mermin they write: I tried to derive equation (11.30) but got stuck on something, I hope someone can help me with it. I'll write below my attempt at deriving equation (11.30). First, notice the following few equations on pages 206-207: $$(11.24) \ \ \ \ \...

Homework Statement I am actually following the derivation of the wave equation from Maxwell equations. And I do not understand one step, because in the task for the derivation I get a slightly different result (maybe they are equivalent, but I am not sure). Homework Equations In the attached...

In SR, fundamental concepts velocity, acceleration, force, momentum were defined as four-vectors. https://en.wikipedia.org/wiki/Four-vector Does someone show me a derivation of the equation E = mc2 from those definition?

If there is a net force along the y-axis, i.e. T sin(θ2) - T sin(θ1) Why is it equals to ma, where a is the acceleration of the piece of string along the y-axis? Shouldn't there be a torque so the piece of string rotates? Sorry for sounding stupid.

Hi, I'm studying Choppers and I'm struggling with derivation of Buck Converter. As per equation 13.3 if I solve it ahead I get Vs D T - Vo D T = - Vo T + Vo D T Solving this ahead I get Vs (D T ) = Vo (-T + DT + DT) Vs (DT) = Vo(2DT - T) Vs D = Vo (2D - 1) Vo / Vs = D/(2D - 1) Not sure how to...

I am having a very difficult time verifying the equations for full differential amplifier. I literally read all the articles I can find from Google. Here is one of the question I think the paper by Jim Karki is wrong. The equation is equation (9). I verified the rest of the equation already...

Homework Statement Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.Homework Equations The form of the L. density is: $$L=-\frac{1}{2} (\partial_n A_m)(\partial^n A^m) - \frac{1}{c} J_m A^m$$ where J...

Would someone explain the last step in eq.(2.34) in Heald and Marion? Much thanks ahead.

Homework Statement Derive the bernoulli binomial distribution.Homework EquationsThe Attempt at a Solution Each bernoulii trial could have only two possible outcomes . Let’s name one outcome as success and another outcome as failure. Let’s denote the probability of getting success and failure in...

Mentor note: Thread moved from homework sections as being a better fit in the math technical section. Multiplying components of both sides are also off limits. I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) -...

Hi. Here, somebody apparently derives Maxwell's equations using only symmetry of second derivatives and the Lorenz gauge condition. Unfortunately it's in German, but I think the basic ideas are clear from the maths only. In this derivation, the magnetic field turns out to be divergence-free...

Hello PF, I was doing the derivation of the Lagrange equation of motion and had to do some calculus of variations. The first step in the derivation is to multiply the integral of ƒ(y(x),y'(x);x)dx from x1 to x2 by δ. and then by the chain rule we proceed. But I cannot understand why we are...

Hi, I'm struggling with source-free RL Circuit derivation. In the books in the right side diagram they've reversed polarity of inductor to get equation: V(r) = - V(L) But why? I checked google and everywhere they had put inductor with positive sign upwards. Here is what I think-- In left...

Homework Statement I need to find the intial velocity of a ball, given the angle the pendulum bob swings through. I need to derive this equation. [/B] V0=4.43mtotalL1/2{1-cosΔθ}1/2/mball Homework EquationsThe Attempt at a Solution I have barely any attempts since I can't even think where to...

Hello Everybody, I am Meaningless and I had this doubt on Newtons laws of gravitation while deriving it. My textbook stated the following derivation 9 for any two masses m1, m2, and radius 'r' It stated that according to the law of product of masses...

I am trying to understand the derivation of the Casimir energy from https://en.wikipedia.org/wiki/Casimir_effect#Derivation_of_Casimir_effect_assuming_zeta-regularization. At one point, the derivation writes the following: The vacuum energy is then the sum over all possible excitation modes...

Homework Statement Consider the Fourier series of a signal given by $$x(t)=\sum_{k=-\infty}^{\infty} a_ke^{jk\omega_0t}$$ Let's consider an approaches to this series given by the truncated series. $$x_N(t)=\sum_{k=-N}^{N} a_ke^{jk\omega_0t}$$ a- Show that if $x(t)$ is real then the series...

Homework Statement Homework EquationsThe Attempt at a Solution My question is how to derive ##(4.13)## from the above preceding paragraphs?, I am not sure how achieve these terms.

Homework Statement I have derived the expression for the velocity of the satellite v= root of GM/r however I'm struggling to derive an expression for the centripetal acceleration of a satellite orbiting Earth. Homework EquationsThe Attempt at a Solution I'm not entirely sure which equations to...

Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a very rough tabletop as shown below, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block A is then released from rest at a...

Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...

Homework Statement From pages 10--11 in "A First Course in General Relativity" (Second Edition) by Bernard Schutz: Given $$\Delta\overline{s}^2 = \phi\left(\textbf{v}\right)\Delta s^2,$$ where ##\Delta \overline{s}^2## is the interval measured between two events in frame ##O'##, which is...

I am puzzled by the derivation of the Cantor set. If the iteration of removing the middle-thirds leaves an uncountable set of points, it seems the iteration had to be performed an uncountably infinite number of times. Is this the case? If so, that seems paradoxical to me.

I tried to derivate pi using calculus but i just found a quite different result. Can you spot my wrong please?First i started with equlation of a circle which is: $$x^2+y^2=r^2$$ I am assuming circle's center stands on the center of origin. To reach pi we shoud consider the situation that...

Homework Statement [/B] I have been given an equation for the magnetic potential of a buried magnetic object which is as follows Pm=α/x2 Where α is some constant and x is the distance from the magnetic body. I need to derive an expression for the magnetic field strength at some distance x...

<Moderator's note: Moved from a technical forum and therefore no template.> Hi everybody I've been trying to solve this problem all the afternoon but I haven't been able to do it, I've written what I think the answers are even though I don't know if they're correct, so I've come here in order...