Euler Definition and 387 Threads

Hi everyone :D This is my problem: Find conditions on \alpha and \beta in the Euler equation x^{2}y'' + \alphaxy' + \betay = 0 such that: a) All solutions approach zero as x \rightarrow 0 b) All solutions are bounded as x \rightarrow 0 c) All solutions approach zero as x \rightarrow\infty I...

Can someone explain "Euler" angles? From what I read, "Euler" rotations are composed out of matrices like * * 0 1 0 0 * * 0 * * 0 0 * * * * 0 0 0 1 0 * * 0 0 1 which is pretty distinctive in that they rotate around same axis twice, and makes sense for devices like this...

[SOLVED] Euler Lagrange Equation Hi there , I am missing a crucial point on the proof of Euler Lagrange equation , here is my question : \frac{\partial f}{\partial y}-\frac{d}{dx}\left(\frac{df}{dy^{'}}\right)=0 (Euler-Lagrange equation) If the function "f" doesn't depend on x explicitly...

Let's say you have some type of simplicial complex that is made only of 2 simplices. What happens if all those 2 simplices are adjacent to a single edge (creating a type of book shape), so that this complex can only be embedded in dimensions 3+? Would this complex have the same 2nd betti number...

i have an orientation of a 3d object in space given by theeta, si and phi i.e. angles which the objects makes with respect to three axis. Now i want to translate the problem such that i get an arbitrary axis rotation about which to some calculated degrees would produce same orientation...

Homework Statement Find the general solution of x^2y" - 2y = 0 Homework Equations The Attempt at a Solution Can anyone tell me how to find the general solution of the Euler Cauchy equation. How do we make it into one?? Thanks.

I have a number of objects (points) in a 3D space. I need to rotate this space using euler angles (or equivilent) and place it in another coordinate system. (ie i start with objects placed within the confines of a cylinder aligned with the z axis, and after rotation have a cylinder of objects at...

I was wondering how I would go about proving this equation: \int_{1}^{\infty}\frac{u-[u]}{u^2}du=1-\gamma where \gamma is the Euler Constant, and [u] is the floor function

Is the Euler line in triangles USEFUL for anything in real life? This is the line which contains the concurrency points for the intersections of the triangle perpendicular bisectors, the medians, the altitudes, but not the angle bisectors. Interesting stuff, but are these points which occur on...

i was asked to calculate the integral: \int\frac{dx}{x+\sqrt{x^2-x+1}} by using euler substituition (i.e, finding a line which intersects sqrt(x^2-x+1) through one point and then the equation of the line will be y-y0=t(x-x0) where (x0,y0) is one point of intersection, and then substituing x for...

This may be a stupid question, but I do not understand why the Euler sum is infinite for zeta=1. Why is "1+1/2+1/3+1/4+... " infinite, but zeta=2 (1+1/4+1/9+...) not?

Hi everyone, I am trying to get an intuitive grasp of the Euler Relationship e^i(theta)=cos(theta)+i sin(theta) and also understand how to graph the exponential spiral, as demonstrated on this web page: http://www-math.mit.edu/daimp/ComplexExponential.html" Ok, first the neuron...

Hi i am reading about signal and systems course . What i want to prove is not a problem that i have to solve is something that the books take for granted and i want to prove it so i ll be able at exams to reprove so i won't have to remember it, (if u don't believe me i can give u the course's...

I went off on my own to study the Euler caracteristic + orentability caracterisation of closed surface and I must have gotten lost somewhere, because I do not find that the Klein bottle is homeomorphic to \mathbb{R}P^2\#\mathbb{R}P^2 as I should. I started with the result that for two surfaces...

(a) Let alpha (a) and beta (b) be given constant. show that t^r is a solution of the Euler equation t^2 d^2y/dt^2 + at dy/dt + by = 0 , t>0 if r^2 + (a-1)r + b = 0 (b) suppose that (a-t)^2 = 4b. Show that (ln t)t^(1-a)/2 is a second solution of Euler's equation. please help, i have no idea...

In "Dr. Euler's Fabulous Formula" by Paul Nahin, early in chapter 1 is discussed characteristic polynomials of a square matrix and the Cayley-Hamilton theorem, that any square matrix A satisfies its own characteristic equation. On page 21 it states p(lambda) = lambda^2 + a1*lambda + a2 = 0 and...

I've been trying to do some simulations using the Euler, improved Euler, and Runge-Kutta methods. My results for the improved Euler and Runge-Kutta are very close to my results with the plain old Euler method. If there is any improvement, it is negligible. This lack of improvement surprises...

Homework Statement For fun: show that B(a,b) = \int_0^1{x^{a-1}(1-x)^{b-1}\,dx} = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} where a > 0 , b > 0 . Hint: start from the product \Gamma(a)\Gamma(b) and switch to polar coordinates. The radial integral is proportional to \Gamma(a+b).Homework...

"Euler" was pronounced with a long "u" sound Ok, Up until last week I thought "Euler" was pronounced with a long "u" sound (like Euclid). Since most of the famous names of science/math are names I have read, not heard, I was wondering if someone could give me the correct pronunciation of...

Hi, I was wondering if Matlab was the sort of program I'd want to solve the Euler Equations (fluid dynamics). And if it is, I am sure this must be a very standard problem.. does anybody know of any tutorials for this sort of problem as I have never used matlab? :-p

The Euler Function \varphi (n) is defined as the number of natural numbers less than n that are relatively prime to n. That is, \varphi (n) = | \{ a \in \mathbb{N} | a < n and gcd (a, n) = 1 \} | I have been asked to show that if a number d divides a number n, then \varphi (d) divides...

I'm looking for a method to rotate a 3D vector, and place it at an arbitary 3D point (x,y,z) without changing the vectors magnitude. I have briefly investigated eulers angles (mainly through wikipedia links etc), but don't fully understand the process yet. As an example, given the vector ...

Can anyone describe what the effects of the Euler force are? If you're not familar with it, it is a fictitious force that arises from a rotating object undergoing a change in rotation speed. Can someone tell me what the effects of this fictitious force are?

In an anlaogy with the Euler product of the Riemann function we make: \prod_{p}(1+e^{-sp})=f(s) of course we have that: f(p1+p2+p3)=f(p1)f(p2)f(p3) f(x)=exp(-ax) if Goldbach Conjecture is true then p1+p2= even and p5+p6+p8=Odd for integer n>5? then this product should be equal to...

Hi, I would like to see the resemblance between planet Earth and a spherical top. I draw here the x-convention Euler angles as I know them: 24 hours to complete one complete one revolution around it's own z' axes. And the 23.5° Earth axes revolves around the "sun's z axes" - the line...

Can anyone help me solve the following question. ABC is any triangle. XAB, YBC and ZAC are equilateral triangles formed on this triangle. Prove that AY, BZ and CX are concurrent. In a triangle ABC, the Euler line is parallel to side BC. Prove that tanB*tanC = 3. I just need a hint. I...

Hi I'm told that the the following can be presented as a classic euler question: A farmer goes to marked with 1770 dollars to buy rice and corn. One bag of corn costs 10 dollars and one of rice cost 20 dollar. How much corn and rice can the farmer buy? This can be presented in the following...

I'm sure this is relatively easy, but after an hour or so googling, I can't seem to find the formula for generating terms of the http://steiner.math.nthu.edu.tw/chuan/123/test/euler.htm Is this known by some other name? Maybe that's why I can't find it? Thanks

how could v 'calculate' the orbifold euler char. using String theorists' formula for the same ? For example, i know the Euler char. of S^1/Z_2 is 1, when we identify the x to -x points of S^1(not the antipodal points i.e. dimetrically opposite points, but putting a mirror along the horizontal...

I did solve this differential equation (x^4)y'''' + 6x^3y''' + 9x^2 + 3xy' + y = 0 using Cauchy Euler Equation. I got X^m (m^2 + 1)^2 = 0 I'm not sure how to get the roots of (m^2 + 1)^2. In my calculation I got m = -i, +i, -i, +i when I put m^2 = -1. In the book they have m = (+-)...

If a connected graph has a Euler circuit then this implies that all the vertices of the graph have even degree. Is the converse of this argument true? i.e. If a connected graph only contains vertices of even degree does this imply it contains an Euler Circuit? Could somebody please show me a...

Would you please tell me how to improve Euler's approximation to be better in solving differerential equations ? Can you give me some links to this? Thank you,

I think this will be my new mantra ;) but it is actually related to the question. I want to define the sequence (s_n) where n is natural and whose nth term, t_n, is the sum of the digits of n. I want to do this without using Gauss's modular arithmetic. This may be one of those 'easier said...

A uniform circular disk of mass m and radius a is constrained to rotate with constant angular speed omega abotu an axis making an angle theta with the disk' s axis of symmetry. Find the magnitude and direction of the angular momentum L and the torque tau exerted on the disk by its supporting...

can some one explain to me how is taking the logarithm of euler product gives you -sum(p)[log(1-p^s)]+log(s-1)=log[(s-1)z(s)]? my question is coming after encoutering this equation in this text in page number 2...

[SOLVED] Euler 9 point circle I'm doing a project on the nine point circle and i need to know what type of triangle it works with. I tried constructing it but it didn't work with an isoscoles or a obtuse triangle, but a website said it works with all triangles, can anyone help?

Hi Im a bit stuck on the method for Euler Integration. I have the following first order differential equation: dx/dt = (x-at) / (x / a+t) where constant a = 1.0V/s, and initial condition x = 1.0V at t=0s I have a time step of 0.02 and I need to calculate the output voltage at a time...