Euler Definition and 387 Threads

e^{ix}=cos(x)+isin(x) Simple enough? Well I am biting my head off because I don't know how he did it. Why is this bothering me? ex is not a periodic function. How in the world magic happens when you put an i into exponent, and it gets periodic. I want to know this so badly.Why is this...

Expansion 1D Euler Eq.?? Trying to figure out an expansion step for 1D Euler Equations for unsteady gas flow. Continuity: \frac{\partial(\rho F)}{\partial t}+\frac{\partial (\rho uF)}{\partial x}=0 After Expansion: \frac{\partial(\rho)}{\partial t}+\frac{\partial (\rho u)}{\partial...

hi, i am a beginner of this forum. i am not really sure how to use this forum actually. i would like to ask, how to find euler buckling load? what is the formula i need to use?

Hi all, I've formulated using Lagrangian formalism the equations of motion for a spinning top. I know about the gimbal lock/singularity that occurs at theta=0 and I was wondering if there was any other way to do it without dwelving into quaternions. Yogi published a paper "A Motion of Top...

The definition of the Euler - Mascheroni constant, \gamma, is given as \gamma = \lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k} - \ln(n) or equivalently in integral form as \gamma = \int_{1}^{\infty}\frac{1}{\left\lfloor x\right\rfloor} - \frac{1}{x}\ dx I saw a seeming related integral...

Who are the current greats that will go down as "Gods equal to Gauss, Euler, etc.)? Each generation of mathematics (dunno how long a generation is) have great mathematicians. Last generation was Hilbert, Poincare, cantor, and prolly 1-2 more. Alot of the works that these mathematicians have...

so i know for example that d/dt (∂L/∂x*i) = ∂L/∂xi for cartesian coordinates, where xi is the ith coordinate in Rn and x*i is the derivative of the ith coordinate xi with respect to time. L represents the lagrangian. so using an arbitrary change of coordinates, qi = qi(x1, x2, ..., xn) i...

Anyone know any good sources to read about Euler substitutions from? Both online and books would be suffice. Also videos, if there are any. All help would be greatly appreciated =)

Yeah is there any correlation between being single for the rest of your life and very successful in Math/physics?

Hi guys, could you please help me out? Essentially, a laser is pointing at a certain point in 3 dimensional space. There is a fixed target that the laser is specifically supposed to point to. My job is to find the most efficient way to solve for the euler angles(yaw pitch and roll) in order...

I've successfully (well I think so) made 2 different programs that can numerically solve an ODE using Euler and Runge-Kutta's methods. Here they are: program test implicit none real(8)::a,b,h,y_0,t write(*,*)"Enter the interval a,b, the value of the step-size h and the value of y_0"...

1. I have a complex Ohm question in which u(t) is given as Umax*\sqrt{2}cos(\varpi+\varphi), i know how to convert from trigo to euler form if i have both sin and cos but this doesn't. Is it possible to convert just a cos to Euler form ? 3. Since it is a complex impedance i tried to...

Hi All, is there anybody to give me some help on how I can calculate the Euler Lagrangian equation associated with variation of a given functional? I am new with these concepts and have no clue about the procedure. thanks a lot

hello, I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a...

Homework Statement Since the exercise has a graph I uploded it here :http://imageshack.us/photo/my-images/833/img9845wz.jpg/ fmax(t)=1 T=2Pi h=1,3,5,7,... Also I was told that I could use Eulers formula here. Homework Equations maybe someone could give me some tips how to make the...

Homework Statement Solve the IVP (x^2)y'' + 4xy' - 40y = x^6 for y(1) = 10, y'(1) = 1Homework Equations not so much "equations" but here I try to use variation of parameters to get the particular solution.The Attempt at a Solution FOR THE HOMOGENEOUS SOLUTION: using the substitution y = x^r...

Homework Statement The implicit Euler method is yn = yn-1 + hf(xn,yn). Find the local truncation error and hence show that the method is convergent. Homework Equations The Attempt at a Solution I found the error to be ln = (-h2/2)y''(xn-1) + O(h3). For convergence I am up to...

Fairly straight forward question. If you have a set of three vectors specifying a frame of reference and a second set of 3 vectors stating another frame of reference. How do you get the Euler angles associated with that rotation? More generally I am considering the relative orientation of one...

Hi Everybody I am beginner in c++ and I need your help please. I implemented euler method for solving simple ODEs (y' = x -y, y(0)=1)and it is forward in time(from t=0 to t=1) and it worked well, my question is : I want to run this code backward in time(t=1 to t=0) what i have to change in my...

Hello there, I was wondering if anybody could indicate me a reference with regards to the following problem. In general, the Euler - Lagrange equation can be used to find a necessary condition for a smooth function to be a minimizer. Can the Euler - Lagrange approach be enriched to cover...

a steel rod, 40mm in diameter and 1.00m long, is pinned at each end i) calculate the euler buckling for the rod ii) identify three other possible end fixity conditions for the rod and demonstrate how euler buckling load would be affected in each case iii) explain the relation between the...

Hello there, I am dealing with the functional (http://en.wikipedia.org/wiki/First_variation) J = integral of (y . dy/dx) dx When trying to compute the Euler Lagrange eqaution I notice this reduces to a tautology, i.e. dy/dx - dy/dx = 0 How could I proceed for finding the y(x) that...

Homework Statement Hi there. I'm not sure if this question corresponds to this subforum, but I think you must be more familiarized with it. The thing is I don't know how to get from: M_x=(I_0-I)\dot\Psi^2\sin\theta\cos\theta+I_0\dot\Phi\dot\Psi\sin\theta to...

Prove that the Euler phi equation is always divisible by 2. If n > 2.? I don't understand how this proof works: I think I need to show that the inverse of a and a are both generated by the same group. Therefore, there are at least 2 elements that generate all other elements in the group...

Hi, I recently need to do some numerical simulation by Euler method to solve a PDE. However, I noticed that there are some errors which are obtained with bigger numerical steps, when applying Euler scheme. Since my major is not mathematics, I do not know what this phenomenon is called. I...

Euler Lagrange Equation : if y(x) is a curve which minimizes/maximizes the functional : [SIZE="4"]F\left[y(x)\right] = \int^{a}_{b} [SIZE="4"]f(x,y(x),y'(x))dx then, the following Euler Lagrange Differential Equation is true. \frac{\partial}{\partial x} [SIZE="4"]-...

Homework Statement If L(y, y', x) = y^{2} + y'^{2} then find the appropriate Euler Lagrange Equation. I have absolutely no idea how to solve this. I used the differential form of the Euler Lagrange equations for a stationary action but the answer i got was nothing like the answer in the book...

For weeks I've been coding a program to simulate waves on a string. Currently I am working on some numerical methods. Namely Euler and Runge-Kutta. I have Euler working fine as far as I can see for a variety of input waveforms (of course after it runs for a while it goes a bit beserk due to...

x^2 y'' + x y' + n^2 y = 0 \; Is Euler equation and solution is y=x^m I understand the three cases with different solution. But my question is if n=0. If I use y=x^m \;\Rightarrow\; m(m-1)+m=0 \;\Rightarrow m^2 = 0 \;\Rightarrow m=0 That would not work. I know the answer is y=C_1...

Homework Statement x^3y'''-3x^2y''+7xy'-8y=x+e^2x Edit : Got it thanks

Hello guys, I am new here to the forum and I was wondering if you could help me with some trouble I am having with differential equations. For your information: I am a second year applied physics student from the Netherlands and I loveee everything about physics and mathematics! The problem...

my book says that it is actually difficult to get the true motion of a body by using these equations because it says that euler equations are written in embedded axis frame ... what is an embedded axis frame?where is it different from normal frames that i used in before?after solving euler...

Do 10 steps. Solve the problem exactly. Compute the error (Show all details). The problems says do 10 steps, but 3-4 steps will suffice! Problem: y(prime) = (y-x)^2 y(0) = 0 h = 0.1 I don't understand how to get the exact solution and what to do from there! I know that, f(x,y) =...

Suppose we have the differential equation: \frac{dx}{\sqrt{1-x^2}} + \frac{dy}{\sqrt{1-y^2}} = 0 It can be rewritten as: \sqrt{1-y^2}dx + \sqrt{1-x^2}dy = 0 One solution of this equation (besides arcsin(x) + arcsin(y) = C), is given by: x\sqrt{1-y^2} + y\sqrt{1-x^2} = C...

Hi.. The wikipedia article on euler angles claims that the Euler angles in zxz convention are unique if we constrain the range they are allowed to take (except in the case of the gimbal lock). This seems reasonable. But can someone give me a reference... a book or a paper where this is...

I have multiple robot cells that i would like to move fixtures from robot to robot with the out come of the part to be perfect. in order to do that i need to make sure my work object is in the same spot each time. so i need to find the yaw pitch and roll and convert them into Euler angles. On...

I have derived an explicit formula for the http://mathworld.wolfram.com/EulerZigzagNumber.html" , the number of alternating permutations for n elements: A_j=i^{j+1}\sum _{n=1}^{j+1} \sum _{k=0}^n \frac{C_k^n(n-2k)^{j+1}(-1)^k}{2^ni^nn} For details, please refer to my article in...

HI there, I am having problems understanding something. If I have an axis pointing towards the galactic north pole, and I rotate it using an Euler rotations how can I can I establish the rotation angles needed so that it will be pointing to the equatorial North pole. I am looking for...

Hello guys, I'm trying to find an algorithm to solve an overlap problem between many polyhedra in space, so here this question appears. Imagine an Ellipsoid rotated by Euler angles in 3D space. This Ellipsoid could be characterised by its 3 radii Rx,Ry and Rz, and by 3 Euler angles in...

I was wondering if the Euler buckling method is simply theoretical or actually accurate in the real world. I am asking this both for complex structures and a simply compressed rod or beam. Thanks

I'm looking at the following example (http://www.cyclismo.org/tutorial/matlab/control.html): y'=x^2-y^2, y(0)=1, where they use the Euler method to approximate numerical solutions. This is the code: I don't understand the third and fourth line at the top. What is y = 0*x and how did they...

Every textbook i find breezes over the following point: \delta\partial (x) =\partial \delta (x) where delta is just the variation. Someone asked me why that's true and i guessed the only thing i could say was that delta is an operation not a variable so this is more like an algebraric...

hi guys, can someone give me a quick tutorial on how to solve and explain to me the concept of slope field of the following differential equation: sketch the slope field for dy/dt = 2t+1 showing the solution y=t^2+t-4, which satisfies the initial condition y(-2)= -2 Also how to use...

Hello every one, I am a new comer. During my research of ionization rate of molecule using ADK method, I meet a question. What is the rotation matrix and R the Euler angles between the molecular axis (in Eq. (8) of reference PHYSICAL REVIEW A, 66, 033402 (2002)) and what form is the...

How do you guys deal with the fact that even though you enjoy Mathematics or Physics, you will probably never be the next Euler, Gauss, Nash, Einstein, Feynman etc? It really puts me off reading about how talented these people were. Sometimes i just feel redundent. I will get frustrated when...

Homework Statement determine the gen sol of the DE x^2y'' - 5xy' + 9y = 0 Q/P = A = -5 and R/P = B = 9 then use y = x^r in original DE... y' = rx^(r-1) y'' = (r-1)rx^(r-2) insert into DE x^2 (r-1)rx^{r-2} - 5x(rx^{r-1})+ 9x^r = 0 i am confused as to how to proceed...

The Euler Characterisitc can be computed from the dimensions of the Z homology of a space. Are there any other invariants that can be computed from the dimensions of the Z homology?

I should probably know the answer to this but anyway... I want to compute the critical buckling load for a simple 3D rectangular cross-section beam, though the thickness in the z-direction is small. If a load is applied in the negative y direction, which direction do I use for my...

I am having trouble with this proof: show that if d|n then phi(d)|phi(n). I know that if d|n, then ad=n and that phi(ad)=(a,d)*phi(a)&phi(d)/phi((a,d)), but I can't seem to get anywhere with this info. Thanks for your help.

Matlab Help! Euler method Use Euler's method: cooling constant r = 0.2 , initial temperature of 86 C, and room temperature at 17 C. Choose your time step h and integrate to 5 minutes. You can add some cream which will drop the temperature instantly by 5 C. (a) Now, add the cream at the...