Euler Definition and 387 Threads

Is it possible for an Euler equation to satisfy the boundary conditions Y(1)=0, Y(2)=0? I have considered the three possibilities, distinct real roots, repeated roots and conjugate complex roots and cannot find any solutions. Are there any other possibilities to consider? Thanks

Dear everyone can anyone help me with the euler lagrange equation which is stated in d'inverno chapter 11? in equation (11.26) it is said that when we use the hilbert-einstein lagrangian we can have: ∂L/(∂g_(ab,cd) )=(g^(-1/2) )[(1/2)(g^ac g^bd+g^ad g^bc )-g^ab g^cd ] haw can we derive...

Hi, I would like to start from the stress energy tensor for the perfect fluid: T^{\mu\nu}=\begin{pmatrix} \rho c^2 & 0 & 0 & 0\cr 0 & p & 0 & 0\cr 0 & 0 & p & 0\cr 0 & 0 & 0 & p\cr\end{pmatrix} where \rho is the mass density and p is the pressure, and I would like to derive the...

Given the homogeneous equation: x3y''' + 15x2y'' + 61xy' + 64y = 0 I get 3 solutions which are all -4. Does this mean that the solution for y should be: y = c1x-4 + c2x-4lnx + c3x-4ln2x ?

What would be the euler angles of rotation 2pi/3 about the line x=y=z? If something were in the xy plane and it underwent that rotation, would it end up in the yz plane?

Homework Statement This is a problem that the book uses as an example and I've been trying since friday to get the same answer but i have not had any success, i need help :( Well in this problem, F = y(1+(y')^2)^1/2 Homework Equations eulers eqn d/dx(partial(F)/partial(y')) -...

I am a self studier, there might be things seems obvious to you guys that are not obvious for me. I have a few questions here, I write down the equation first and present the question in the last part. Please bare with me. Thanks. Eulers equation of 2nd order: L[y]=x^{2} y''+ \alpha xy'+...

Greetings, I am trying to implement backward euler implicit method by Newton-raphson iteration. The differential equation is for a simple planar pendulum. So the function for the pendulum is : (1) angularAcceleration (angle) = ( -gravity/length ) * sin(angle); and the update function for...

Homework Statement in fortran 90 write a program to using the euler scheme to solve the differential equation for decay of a radioactive substance dx/dt = -j*x solving the equation we get x = e^(-j*t) following info is given 2. Homework Equations and values t0 = 0.0 tF =...

I am confused by both of these. I get what it does, and how it does it, but when using it, somehow I ultimately screw up. Could someone just post a quick description of what to do in conversational English, please? I am pretty sure that would solve this random mental block I have...

Hi all, I am trying to implement the backward euler integration (in c++) for the pendulum problem. I have the forward euler implemented, but frankly I don't know where to even start from for the implicit integration. I understand the update expressions for implicit, and of course the...

Hi, Can anyone show me what´s the deduction for e Euler number ? Thank you

So I registered on http://projecteuler.net/" and I must say: it's quite addictive! I didn't expect it to be that much fun. I'd like to share what things I've learned from solving the problems: - When solving a problem you get access to a thread. I was impressed how different the...

What is the largest prime factor of the number 600851475143 ? My attempt: #include <stdafx.h> int main() { int num1, num2, num3, num4, lrgprime, sum; lrgprime=num2=num4=sum=0; for (num1=2; num1<300425737572; num1++) { num2=600851475143%num1; if (num2==0) { for...

im trying to do the Euler problem #14 - to determine which starting value under one million produces the longest chain and here's my code in Python Count=[] Count2=[] List=[] def seq(n): if n%2==0: return n/2 else: return 3*n+1 m=1 for i in range(1,1000000): j=i List.append(j) while...

Hi all, I'm having trouble understanding a basic concept introduced in one of my lectures. It says that: To solve the DE y(t) + \frac{dy(t)}{dt} = 1 where y(t) = 0, using the Euler (forward) method, we can approximate to: y[n+1] = T + (1-T)y[n] where T is step size and y[0] = 0...

Homework Statement Solve the euler differential equation \x^{2}y^{''}+3xy'-3y=0 \int_X f = \lim\int_X f_n < \infty by making the ansatz [tex]y(x)=cx^{m}[tex], where c and m are constants. The Attempt at a Solution [tex]y(x)0=c^{m}[tex] [tex]y^{'}(x)=cm^{m-1}[tex]...

I'm reading a book called The Road to Reality by Roger Penrose, and I'm on the chapter for complex logarithms. What I don't understand is how the identity e\theta i = cos \theta + i sin \theta is found through the use of complex logarithms. I also don't understand how if w = ez, z = log r +...

Homework Statement i need to obtain the remainder of the divison 2^{1000005} divided by 55 Homework Equations Euler theorem 2^{\phi (55)}=1 mod(55) The Attempt at a Solution my problem is that applying Euler theorem i reach to the conclusion that the remainder is the...

Homework Statement Hi, I'm trying to compute the equations of motion for a car as shown in the attached image. α = steering angle θ = orientation of the car relative to the world coordinate system Say you're given the linear velocity v and the steering angle α. How do you compute...

Hi, I'm trying to compute the equations of motion for a car as shown in the attached image. α = steering angle θ = orientation of the car relative to the world coordinate system Say you're given the linear velocity v and the steering angle α. How do you compute the position and angle...

Hi, I need to solve the following simple ODE with both the Euler Forward and Euler Backward numerical methods. I also need to answer for which values of T this can still be calculated: y'(t) = \frac{-1}{2y(t)} y(0) = 2 t \in (0, T] Obviously the analytical solution is y(t) = \sqrt{4 - t} So it...

Hello, I am trying to extract the 3 angles from a unit vector to position a part on a 5 axis milling machine: This machine has 3 linear axes (x,y,z), direct coordinate system It has 2 rotary axes: A turns about the x (called 'tilt') C is carried on the A axis (called 'rotary') See...

Homework Statement I want to find the euler buckling for a open I beam( middle section like a box) that is subjected to three point bending with a point load on top. I am not so interest in a solution but explanation on how this could be worked out using the euler equation for buckling...

Homework Statement Prove that the rate of convergence for Euler's method (in solving the problem y'=y) is comparable to 1/n by showing that lim_{n\rightarrow infinity} \frac{e-(1+\frac{1}{n})^n}{1/n}. Homework Equations Hint: Use L'Hopital's Rule If lim x-> infinity f(x)/g(x) is in...

Could somebody explain to me how lagrange multipliers works in finding extrema of constrained functions? also, what is calculus of variations and lagrangian mechanics, and can somebody explain to me what the lagrangian function is and the euler-lagrange equation. And, i read something about...

Q- Let m and n be coprime. Show that\phi(mn) = \phi(m) * \phi(n). Hint: when does a pair of residues modulo m and n have an inverse.

1. I use Euler formula of arctan to calculate arcsine 2. This equation\arctan x = \frac{x}{1+x^2} \sum_{n=0}^\infty \prod_{k=1}^n \frac{2k x^2}{(2k+1)(1+x^2)}. If I input 0.9999999999, I will not be able to get the expected result. If input = 0.9 then it is pretty correct, but 0.99 is definitely...

Homework Statement Well, the question is to find a formula for \phi(p^n) where \phi is the Euler's totient, and p is a positive prime. Homework Equations \phi(2^n) well in this case here is what i did, i first took n=1, n=2, n=3, and it looks like \phi(2^n)=2^{n-1} but i am...

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

Is it possible to prove Euler's identity (e^i*pi = -1) without simply taking it as a special case of Euler's formula (e^i*x = cos(x) + i sin(x))?

Hello, can anyone help with this question? Thank you. Let n even perfect number and q prime. Show that n/Φ(n)=2q/q-1. Φ(n) is the Euler function-totient (the number of positive integers less than or equal to n that are coprime to n) I have tried euler-euclid theorem but could not...

Euler Method in Fortran - HELP! Using Euler method I want to calculate the equation below, deltat=0.3, 10 times. Problem: When n=1, Yn1(1) is calculated right. But, in the following steps it should assume that Yn(2)=Yn1(1) and the program is assuming Yn(2)=0, as well as Yn(3)=0,...and so on...

although is not valid in general (since an Euler product usually converges only when Re(s) >1) \frac{ d \zeta(1/2)}{\zeta (1/2)}= -\sum_{p} log(p)(1-p^{1/2}

I'm stumped on a HW question that I just can't seem to proceed on. Homework Statement An incompressible ( rho = constant ) flow in 2 dimensions [x = (x,z)], with F = (0,-g), satisfies Euler's equation. For this flow, the velocity is u = (u0,w(x)), where u0 is a constant, with w = 0 on x...

firstly, all d's i use will mean partial derivative 'do' because i don't have the font installed. sorry :( please help me with these.. u got to use euler theorem 1. if z= xf(y/x) + g(y/x), show that x2(d2z/dx2) + 2xy(d2z/dxdy) + y2(d2z/dy2) =0 2. if z= (xy)/(x-y), PT (d2z/dx2) + 2(d2z/dxdy)...

Hi all Im working on a systems dynamics problem which involves modelling a double pendulum, a chaotic system I have a non linear system of 4 1st order differential equations which I need to solve using numerical methods in MATLAB The methods are ode45, ode23s and euler method Ive...

Dear All, Suppose you have two versors x and y. You would like to calculate the 3 Euler angles between them. How would you do that? You know that x=Ry where R is the rotation matrix (see e..g Goldstein). Now the point is that I know both x and y and want to get phi, theta and psi (no...

The functions K maps to f(K) and C maps to U(C) are given as: F(K) = aK and U(C) = -C^2 +b here a and b are positive constants. the initial and teriminal conditions with the triminal time T = 1/a are K(0) = K_0 and K_T = K(1/a) here K_0 and K_T are positive constants. Write Euler...

Trying to implement QR decomposition using Givens rotations, I calculate G1 to zero n32 of original matrix A, then G2 to zero n31 of G1 * A, then G2 to zero n21 of G2 * G1 * A. Residual matrix, R = G3 * G2 * G1 * A comes upper triangular as expected, so I believe my code is correct. Looking...

can anybody please clearly explain me the difference between these two frames of reference with few examples. my exames are closing up. please help me.

I'm so confused on how to tackle this problem: 1. Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows: Let p be “The object belongs to set A. “Let q be...

Hi, I don't know if this is the right forum to adress, but I will try nevertheless Im solving a simple two-dimensional differential equation: dx/dt = (-y,x) which will give a circle when integrating over time. Now, the problem is that the simple euler scheme seems to be a lot more...

In the general DE form, y"+y=0 and where the initial conditions are y(0)=2 and y'(0)=0, Euler realized that y(x)=e^ix+e^ix. How did he know that it's a cosine graph when there's no indication in the equation that any solution is possible? y= c1+c2=2 but y" gives 0.

Prove that if d divides n then phi(d) divides phi(n). Thanks

I'm trying to follow a professor's notes for finding Christoffel symbols for a two-sphere. He gives the following two equations: The Lagrangian for a two sphere:L = \left( \frac{d\theta}{ds} \right)^2 + sin^2\theta \left( \frac{d\phi}{ds} \right)^2 The Euler Lagrange equation: \frac{d}{ds}...

I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.

Direction field Do anybody have a hint for drawing direction field of a non-autonomous differential equation? I mean do I have to calculate as many slopes of points as possible, then draw it? Also, Can I conclude that if we use Euler's Method to estimate a CONCAVE UP/ CONCAVE DOWN...

Simple question, I have used the euler expansion to estimate a variable that grows as a single exponential. adapt = Amax * exp(-tau*X); In excerpted form: for (i=1;i<npts; i++) { adapt[i] = adapt[i-1] + (Amax -adapt[i-1]) * dt / tau; } where dt is the step size and tau is...