Euler Definition and 387 Threads

My question arises in the context of bosonic string theory … calculating the number of dimensions, consistent with Lorentz invariance, one finds a factor that is an infinite sum of mode numbers, i.e. positive integers … but it really goes back to Euler, and his argument that the sum of all...

The "improved" Euler method Homework Statement Using it on a programming assignment. The description in our course notes is a little confusing, so I need to know whether I'm doing it correctly. Homework Equations Go to p. 22 of this, if you're so inclined...

1. Homework Statement Linearize the euler equations of fluid motion, write as a single partial differential equation for example the pressure pertubation Homework Equations The euler equations of fluid dynamics The Attempt at a Solution Not sure how I would be able to do this.

Homework Statement Dear all, please help. I have tried this question and came up with strange numbers, my fortran is definitely not correct. Please help! When the effect of the air resistance is taken into account, the equation of motion for a particle of mass m falling vertically in a...

Folks, Searches of Timoshenko and Euler Bernoulli Beam Theory show differential equations for straight beams. Is there any material out there illustrating differential equations for "curved in plane beams"..? Thanks

Suppose we have Asec(x) on the right hand side in a non-homogenous ODE and in a Euler equation. How do we solve it? ( I know how to solve for cos and sin on the right hand side but not for any other trig function).

I know how we solve ODE's and euler equations in which we have cos and/or sin terms on the right. We take the particular solution to be Acos(x) + Bsin(x). But what if we have secant or cosecant terms on the right or tan and/or cotangent terms? Qno. 1 Are these 4 terms possible i.e. can they...

Here is my problem, I have been trying this for a couple of hours. I have sought help with a professor, and yet we still couldn't get it. Here is the question in full. Consider the initial value problem below to answer the following. a)Find the approximations to y(0.2) and y(0.4) using Euler's...

Is "a Euler" or "an Euler" correct? Given the pronunciation sounds like "oiler", which article do we use? Couldn't find the grammar forum!:redface:

Folks, Trying to get some appreciation for what is going on in the attached schematic of 1)Euler bernoulli and 2) Timoshenko beam elements. For the first one, ie the top picture, how was ##u- z \frac{dw}{dx}## arrived at? thanks

Folks, I am trying to understand the balance of units for this eqn ## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)## where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is...

Hello there, I would like to obtain the Green function for the operator F, F [u(x)] = u '''', and the boundary conditions u(0) = u'(0) = u (1) = u' (1) = 0. I am looking for a function G ( x, s ) such that G'''' (x,s) = delta (x-s) (the apecis referring to differentiation w.r.t. x, and...

Consider a vector in 3D. Its projections on two planes, say YX and YZ planes, makes some angle with the vertical axis ( the y-axis in this case). I know these two angles (I call them projected angles). This is the only information I have about the vector. I need Euler angles which when...

A problem on my homework: We learn early on that "the shortest distance between two points is a straight line." Let's prove it...Using the Euler equation, compute the extrema of ∫sqrt(1 + (dy/dx)2)dx from x1 to x2 ...show that this corresponds to lines "y = mx +b". Euler had a lot of...

Hi, How can one use back Euler method for 2nd order d.e? Is it possible this method to be expanded for a system of 4 odes? Thanks

Homework Statement I need to verify an integral representation of the Euler constant: \int^{1}_{0}\frac{1-e^{-t}}{t}dt-\int^{\infty}_{1}[\frac{e^{-t}}{t}dt=\gammaHomework Equations The Attempt at a Solution OK, I'm supposed to use this fact (which I have already proved)...

imagine we rotate a vector centered at the origin with euler angles alpha,beta,gamma. now the question is, can we do this rotation by the means of defining a vector N(which its length is 1).and rotating the vector zeta radians counter clockwise around N? I think it must be possible and I want...

If given a cauchy euler equation (non-homogeneous) equation, does the approach in looking for a particular solution (in order to solve the non-homogeneous part), differ from normal? I am also in general confused about how to assign a particular solution form, in many cases. I have yet to find...

xy''+y'=-x y(1)=0, y(0) bounded (so the natural log, 1/x etc. terms drop out) homogeneous, cauchy euler: y=a+bx variation of parameters, and using the conditions gives y=1-x, I think (i tried this previously and I think this is what I got, I didnt write it down). Very different from what I...

This is an extract from my third year notes on 'Computational Physics': The Euler method is inaccurate because it uses the gradient evaluated at the initial point to calculate the next point. This only gives a good estimate if the function is linear since the truncation error is quadratic in...

I was messing around with Euler’s Identity and I think I accidently disproved it. I would like someone to check my math to make sure I didn’t make any rookie mistakes. \begin{array}{l} e^{\pi i} + 1 = 0 \\ e^{\pi i} = - 1 \\ \left( {e^{\pi i} } \right)^2 = \left( { - 1}...

Hello all, I am having some frustration understanding one derivation of the Euler Lagrange Equation. I think it most efficient if I provide a link to the derivation I am following (in wikipedia) and then highlight the portion that is giving me trouble. The link is here If you scroll...

Hello, I am looking at the proof (Theorem 2.5 (b) Apostol) of $$ \phi (mn) = \phi(m) \phi(n) \frac{d}{\phi(d)} $$ where $$ d = (m, n) $$. Can someone explain how they go from $$ \prod_{p|mn} \left( 1 - \frac{1}{p} \right) = \frac{\prod_{p|m} \left( 1 - \frac{1}{p} \right) \prod_{p|n}...

!Euler transform matrix multiplication help! Homework Statement This may be rather simple but i am really struggling to complete a 3 3x3 matrix multiplication. I NEED STEP BY STEP WORKING!. This would really help me I understand the theory. Basically I have three matrices T1= cosψ sin ψ...

Normally with column vectors, we premultiply rotation matrices if the angles are with respect to fixed axis. Why then do we post multiply if the angles are Euler Angles, angles with respect to the mobile axis?

Homework Statement My question refers to the paper "Topological Sigma Models" by Edward Witten, which is available on the web after a quick google search. I am not allowed to include links in my posts, yet. I want to know how to get from equation (2.14) to (2.15). We consider a theory of maps...

I'm trying to write a code to implement he backwards Euler method to integrate the equation of motion. The sticking point seems to be that the acceleration is due to drag, and thus is dependent on the new position and velocity. I understand the method to be: v_{i+1}=v_{i}+a_{i+1}δ...

Problem: Solve the initial Value: when x=1, y=0 dy/dx = 1 2x^2(d^2y/dx^2) + 3x (dy/dx) - 15y = 0 My attempt: x = e^t dx/dt = e ^t dy/dt = dy/dx * dx/dt dy/dt = x*dy/dx d^2y/dt^2 = d/dt(dy/dt) = d/dt(x*dy/dx) =d/dx(x*dy/dx)*(dx/dt) since dx/dt = x =(x^2*d^2y/dx^2) + (x*dy/dx)...

How to compute \chi(\mathbb{C}\mathrm{P}^2)? This problem is from a class on differential topology, so we have defined the Euler characteristic as the sum of the indices of isolated zeros on a non-vanishing vector field. Off the top of my head, I cannot think of any theorems which really help...

Homework Statement Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequence whose values do not exceed four million...

Homework Statement Find the indicial equation and all power series solutions around 0 of the form xr Ʃan xn for: x y'' -(4+x)y'+2y=0 - apparently one of these solutions is a laguerre pilynomial Homework Equations the indicial equation is the roots of r(r-1) +p0r+q0 where p0=lim(x->0)(...

Lagrange & Euler formalism How we get relation (\frac{\partial T^{(L)}}{\partial t})_{r_0}=(\frac{\partial T^{(E)}}{\partial t})_{r}+\frac{\partial T^{(E)}}{\partial x}(\frac{\partial x}{\partial t})_{r_0}+\frac{\partial T^{(E)}}{\partial y}(\frac{\partial y}{\partial...

1. Solve y'=3t^2y^2 on [0, 3] , y0 = −1, using Euler method and Taylor method of order 3. Compare your solutions to the exact solution. y(t)=(-1/((t^3)+1)) I DONT KNOW WHAT IS WRONG WITH MY PROGRAM! PLEASE HELP =D Homework Equations http://en.wikipedia.org/wiki/Euler_method...

I know this is rather trivial question but it's not homework! I need this as part of a bigger project. What I have to do is rotate my reference frame to another one. I want my new z-axis to be a vector Z=(Z1,Z2,Z3) Following the notation of this wikipage...

I'm struggling to understand what the derivative of an attitude quaternion really is and how to use it. I need it to solve a problem relating to a rotating frame of reference relative an inertial frame. The information I have is a vector of Euler angular velocities (i.e for roll \phi, pitch...

I want to prove that Euler Lagrange equation and Einstein Field equation (and Geodesic equation) are the same thing so I made this calculation. First, I modified Energy-momentum Tensor (talking about 2 dimension; space+time) : T_{\mu\nu}=\begin{pmatrix} \nabla E& \dot{E}\\ \nabla p &...

How do you prove that angular velocity is just the time derivative of each Euler angle times the basis vector of its respective frame? I remember it used to be perfectly clear to me a while back, but now I don't remember how the result was derived, and I couldn't find it in any of my books I...

Homework Statement Let p be prime. Show that p [SIZE="4"]∤ n, where n is a positive integer, iff \phi(np) = (p-1)\phi(n). Homework Equations Theorem 1: If p is prime, then \phi(p) = p-1. Conversely, if p is a positive integer with \phi(p) = p-1, then p is prime. Theorem 2: Let m and...

Need urgent help with euler langrange equation. So I've identified the euler langrange equation in my problem as d/dt (∂L/(∂x: ̇))-∂L/∂x=0 translates to d/dS (∂L/(∂C: ))-∂L/∂C=0 if L is L=43.007 ln(C)-0.0042S^2-3.4339S+1059.37 whereby ∂C:= ∂C/∂S. How do i solve this?? I am stuck.

Let n=79 phi is Euler totient Can you find a number k such as : phi(k)=0 mod 79 phi(k+1)=0 mod 79 phi(k+2)=0 mod 79 phi(k+3)=0 mod 79 ... phi(k+78)=0 mod 79 phi(k+79)=0 mod 79 Good luck!

number theorm -- Euler theorem Homework Statement let be an integer that not divisible by 3. Prove that n^7\equivn mod 63 Homework Equations none The Attempt at a Solution it is suffice to prove that n^7\equivn mod 7,n^7\equivn mod 9, i get n^7\equivn mod 7 by Euler theorem ...

Hi, (attachment with visuals is included) I have a 3-D vector dataset that is measured in a reference frame (measurement reference frame) that is oriented relative to a horizontal coordinate system. In this dataset I have x-y- and z-component data for the vectors relative to a coordinate...

Homework Statement Let U = e^{iG_{3}\alpha}e^{iG_{2}\beta}e^{iG_{3}\gamma} where ( \alpha, \beta, \gamma ) are the Eulerian angles. In order that U represent a rotation ( \alpha, \beta, \gamma ) , what are the commutation rules satisfied by the G_{k} ?? Relate G to the angular...

I have read the section about sphere bundle in Differential Forms in Algebraic Topology,but I still don't understand the Euler class very clear.I don't know how to calculate it for a sphere bundle,for example the sphere bundle of S^2. And I can't work out the exercise at the end of the...

I need help to solve this coursework: MATLAB PROGRAMMING COURSEWORK OBJECTIVES:  Learn to solve engineering problems using MATLAB  Write Euler and Runge-Kutta initial-value ODE solvers  Write a Shooting Method boundary-value ODE solver  Investigate the properties of the solvers ...

Hello there, I am interested in the following matter. Given an ODE, can one always find a functional F such that the ODE is its Euler Lagrange equation? I am thinking at the following concrete case. I have the ODE y' = a y I would like a functional given by the intergral over a...

This is an example from Bott and Tu 's book DFAT(page 125).The example is in the image.I don't understand why can we get the local degree of the section s by constructing an vector field by parallel translation and calculate the rotating number of it.And why the local degree is 2? Could...

Hello Can any1 recommend a book that will show the derivation of the Euler-Lagrange equation. (I am learning in the context of cosmology ie. to extremise the interval). Ideally the derivation would be as simple/fundamental as possible - my maths is not up to scratch!

Homework Statement "Vary the following actions and write down the Euler-Lagrange equations of motion." Homework Equations S =\int dt q The Attempt at a Solution Someone said there is a weird trick required to solve this but he couldn't remember. If you just vary normally you get \delta...

Question: Find y as a function of x: x^2 y'' + 8 x y' - 18 y = x^8 y(1)=3, y'(1)=2 Attempted solution: I found the general equation to be Ax^(-9)+Bx^2+Cx^8. However when I try to solve the initial value problem for this equation I have 3 unknowns.