Hyperbolic Definition and 347 Threads

Homework Statement Consider a particle in one-dimensional so called hyperbolic motion x(t)=\sqrt{b^{2}+t^{2}} where b is a constant. a) Find\gamma(t). b) Find the proper time \tau(t). (assume that \tau=0 when t = 0 c) Find x and v_x as functions of the propertime \tau. d)...

Homework Statement I thought it would be better to attach it. Homework Equations The Attempt at a Solution So for the first part I've found that A^2=the Identity matrix, but from there I don't have much of an idea on how to substitute that into the equation for M and end up with...

So, I'm doing a problem where I take arctanh to a limit, and I was wondering if the arctanh function goes to infinity if the argument inside of the function goes to infinity when passing through the limit.

Homework Statement d/dθ csc-1(1/2)^θ = ? Homework Equations d/dx csc-1(x) The Attempt at a Solution I don't know how to deal with the exponent θ

Hey I didn't understand the transition below, I'd be glad for some help thanks

Hi there. I've been trying to solve the integral of 1/(1+cosh(x)). I use Wolfram to give me a detailed solution but I still don't understand second transformations they use. I've attached a a screen grab of the workings and hoped someone could run through it with me. I've used the tan x =...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Homework Statement What is arcsin(√2)? The Attempt at a Solution sin-1(√2)=a+bi sin(a+bi)=√2 ...expressing as hyperbolic sin function: -i*sinh(-b+ai)=√2 sinh(-b+ai)=-(√2)/i ...using the definition of the sin hyperbolic function: (e-b+ai-eb-ai)/2 = -(√2)/i...

Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic geometry in my spare time and had a simple question about the topic. If a straight line in Euclidean geometry is a hyperbola in the hyperbolic plane (do I have that right?)...

q: http://gyazo.com/297417b9665206ae8e38cb8b5d930a83 I'm stuck trying to find the value of x when TN is a minimum here's what I've tried so far: Let T be the point (a,0) and N be the point (b,0) line of tangent through P: ## y = sinh(x)(x-a) ## line of normal through P ## y =...

What is happening with Hyperbolic Comet C-2012 S1 (ISON)? It is going to crash into the Sun at the end of Nov. Was it downgraded from a Comet? Here is a site that used to track it: http://www.heavens-above.com/Comets.aspx?lat=0&lng=0&loc=Unspecified&alt=0&tz=CET I should be big in the...

I cannot reach the answer for this integral which is part of a bigger question related to discounting investments. I know what the answer to the integral is and have tried all the substitutions and tricks I know. Any pointer would be great! ∫(1/(1+cosh(x))) = tanh(x) + C Thanks, Felix

Hi guys, Can you help me I am stuck: By finding the real and imaginary parts of z prove that, $$|\sinh(y)|\le|\sin(z)|\le|\cosh(y)|$$ i have tried the following: Let $$z=x+iy$$, then $$\sin(z)=sin(x+iy)=\sin(x)\cosh(y)+i\sinh(y)\cos(x)$$ $$|\sin(z)|=\sqrt{(\sin(x)\cosh(y))^2+(\sinh(y)...

i don't know how start. please help. $\displaystyle\int xsech^2(x^2)dx$

Homework Statement The problem: Justify the following equalities: \cot x = i\coth (ix) = i \sum^\infty_{n=-\infty} \frac{ix}{(ix)^2+(n\pi)^2}=\sum^\infty_{n=-\infty}\frac{x}{x^2+(n\pi)^2} I am trying to figure out how to start this. When I insert the Euler identity of \coth (using...

The path described by a constantly accelerating particle is given by: x=c\sqrt{c^2/a'^2+t^2} where a prime denotes an observer traveling with the particle and a letter without a prime a resting observer. If we leave the c^2/a'^2 out it reduces to x=ct, which makes sense. The distance...

Do hyperbolic rotations of euclidian space and ordinary rotations of euclidian space form a group?

This is a fun TikZ picture to play with. \documentclass[convert = false]{standalone} \usepackage[utf8]{inputenc} % Euler for math | Palatino for rm | Helvetica for ss | Courier for tt \renewcommand{\rmdefault}{ppl} % rm...

Homework Statement The question I am trying to answer requires me to find the following: dN/dS ∝ S^−5/2/cosh(r/R) and I am giving the follwing equation in the question. A=4πR^2 sinh^2⁡〖(r/R)〗 The Attempt at a Solution Right I know how to get the S^-5/2 in the top half of the...

The equation of the tower structure is a hyperbola of f(x)=E/(X+F)+G hight=23, and meets ground 11.5m on either side of axis , curve also passes through (4,3) This helps to form 3 equations... Use height to find first equation. Use the points where the tower touches the ground on the...

I have been trying to find a hyperbolic trajectory that has hyperbolic excess speed of 3.944 km/s. However, I can only find ones that would start inside the Earth's crust. mue = 398600 energy = mue / (2 * a) ve = 29.78 vinf = 3.944 = \sqrt{mue / a} I have at least 30 more...

It seems as though the contemporary consensus among cosmologists is that the universe is basically flat and Euclidean: http://en.wikipedia.org/wiki/Shape_of_the_Universe However, Einsteins relativity equations describing events in space-time appear to be hyperbolic...

Homework Statement Prove in hyperbolic geometry: In the accompanying figure M and N are the respective (hyperbolic) midpoints of AB and AC and θ and ∅ are the indicated angle measures. Determine, with proof, which of the following is true: (1): θ=∅ (2): θ<∅ (3): θ>∅ ( stands for phi)...

show that the locus of the point \left(\dfrac{a(cosh\theta + 1)}{2cosh\theta},\dfrac{b(cosh\theta - 1)}{2sinh\theta}\right) has equation x(4y^2 + b^2) = ab^2 working: http://gyazo.com/4c96af128d0293bce7f18029c2f54b0d where have I gone wrong :(

I am trying to build a program in Matlab to solve the following hyperbolic PDE by the method of characteristics ∂n/∂t + G(t)∂n/∂L = 0 with the inital and boundary conditions n(t,0)=B(t)/G(t) and n(0,L)=ns Here ns is an intial distribution (bell curve) but I don't have a function to...

Hi Folks,I have come across some text where f(x,y)=c_1+c_2x+c_3y+c_4xy is used to define the corner pointsf_1=f(0,0)=c_1 f_2=f(a,0)=c_1+c_2a f_3=f(a,b)=c_1+c_2a+c_3b+c_4ab f_4=f(0,b)=c_1+c_3bHow are these equations determined? F_1 to F_4 starts at bottom left hand corner and rotates counter...

Homework Statement A particle of mass m is moving in a repulsive inverse square law force ##\mathbf{F}(\mathbf{r}) = (\mu/r^2)\hat{r}##. Given that ##u(\theta) = -\frac{\mu}{mh^2} + A\cos(\theta - \theta_o)##, 1) Determine the paramters of the (far branch of the)hyperbolic orbit...

Homework Statement Consider the equation 4y^2u_{xx} + 2(1-y^2)u_{xy} - u_{yy} - \frac{2y}{1+y^2} (2u_x - u_y) = 0 Find the solution u(x,y) which satisfies u(x,0) = g(x), and u_y(x,0) = f(x), where f, g \in \mathcal{C}^2(\mathbb{R}) are arbitrary functions. Homework Equations I used...

[SOLVED] Fourier Series Involving Hyperbolic Functions Hello everyone! Sorry if this isn't the appropriate board, but I couldn't think of which board would be more appropriate. I was running through some problems I have to do as practice for a test and I got stuck on one I'm 99% sure they'll...

Will someone help me to understand sinh, cosh, and tanh. I know they have some relevance to hyperbolas and trigonometric identities. Thank you.

I've searched and thought on it for a long time but I couldn't find any mathematical proof or something else about the formula of hyperbolic functions. sinh=\frac{e^{x}-e^{-x}}{2},cosh=\frac{e^{x}+e^{-x}}{2} How do I get these formulas mathematically??

Hello, I see that hyperbolic rotation of frame F' about the (x2,x3)-plane of frame F is identical to a Lorentz transformation, corresponding to a linear motion along x1 of the frame F' with respect to F. Then hyperbolic rotation about (x1,x2) means motion along x3 and hyperbolic...

A spacecraft is on a hyperbolic orbit relative to the Earth with $a = -35000$ km and an eccentricity of $e = 1.2$. At some initial time $t_0$, the spacecraft is at a true anomaly of $\nu_0 = 20^{\circ}$. At some later time $t$, the true anomaly is $\nu = 103^{\circ}$. What is the elapsed...

Homework Statement Hi there! I'm just trying to figure out the Fourier transform of the hyperbolic secant function... I already know the outcome: 4\sum\ ((-1)^n*(1+2n))/(ω^2*(2n+1)^2) But sadly, I cannot figure out how to work round to it! :( maybe one of you could help me... Homework...

Homework Statement Prove that cosh (\frac{x}{2}) = \sqrt{\frac{cosh(x)+1}{2}} Homework Equations cosh(x) = \frac{e^{x}+e^{-x}}{2} The Attempt at a Solution \frac{\sqrt{e^{x}}+\sqrt{e^{-x}}}{2} \ast \frac{\sqrt{e^{x}}-\sqrt{e^{-x}}}{\sqrt{e^{x}}-\sqrt{e^{-x}}} \rightarrow...

Hi all, In studying the eigenvalues of certain tri-diagonal matrices I have encountered a problem of the following form: {(1+a/x)*2x*sinh[n*arcsinh(x/2)] - 2a*cosh[(n-1)*arcsinh(x/2)]} = 0 where a and n are constants. I'm looking to find n complex roots to this problem, but isolating x...

Hi, I am trying to integrate (tanh(x)+coth(x))/((cosh(x))^2) I am substituting u=tanh(x), du=dx/((cosh(x))^2) and end up with 1/2(tanh(x))^2 + ln |tanh(x)| + C which is incorrect. What am I doing wrong??

If the hyperbolic paraboloid z=(x/a)^2 - (y/b)^2 is rotated by an angle of π/4 in the +z direction (according to the right hand rule), the result is the surface z=(1/2)(x^2 + y^2) ((1/a^2)-((1/b^2)) + xy((1/a^2)-((1/b^2)) and if a= b then this simplifies to z=2/(a^2) (xy) suppose...

Hello. I need to estimate height and diameter of a cooling tower. My water requirements are 50000 m3/h, for a cooling duty of about 730 000 000 kcal/h. For this capacity, I thought that an hyperbolic tower, natural draft, would be the best choice. Am I right? Water temperatures in-out would...

Homework Statement Simplify the following expression: arccosh \left(\frac{1}{\sqrt{1 - x^2}}\right) \forall x ∈ (-1, 1) Homework Equations cosh(u) = \left(\frac{1}{\sqrt{1 - tanh^{2}u}}\right) u ∈ ℝ The Attempt at a Solution x = tanhu ∴ u = arctanhx u ∈...

Hello, I am considering the hyperbola x^2-y^2=1 and its intersection with the line y=mx. The positive x-coordinate of the intersection is given by: x=\sqrt{\frac{1}{1-\tan^2\alpha}}=\sqrt{\frac{\cos^2 \alpha}{\cos(2\alpha)}}=\cos\alpha \sqrt{\sec(2\alpha)} where we used the identity...

Hello, I wanted to know why the graph of the hyperbolic cosine function (1/2(e^x)+1/2(e^-x)) looks like a parabola. Is there any reason for this? I suppose the individual exponential functions both go to infinity in a symmetric way... but I wanted a better reason :). Thanks, Mathguy

Homework Statement Consider the points P = (1/2, √3/2) and Q = (1,1). They lie on the half circle of radius one centered at (1,0). a) Use the deifnition and properites of the hyperbolic distance (and length) to compute dH(P,Q). b) Compute the coordinates of the images of Pa nd Q...

Hey everyone, I was wondering what you could tell me about the relationship between hyperbolic paraboloids. I have listed a set of 3 equations and was wondering what I can do with them? Can I solve for z, can I get the intersection of the equations? Can I get generalized solution of any kind...

In Bernard Schutz's 'A first course in General Relativity', p325 (1st edition) he says " [the constant-time hypersurface of a FLRW spacetime with k=-1 (hyperbolic)] is not realisable as a three-dimensional hypersurface in a four- or higher-dimensional Euclidean space." On the face of it...

Homework Statement Compute the following: \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx Homework Equations \int cosh(x)\,dx = sinh(x) + C The Attempt at a Solution I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made u = tanh(\frac{x}{2})...

We have got a series of data points which form a hyperbola. Does anyone know any programs that can get the equation from our points using regression (hyperbola line of best fit). We need to find the equation for investigations with Michaelis-Menten

Hi, I am new to the study of special relativity but think I understand it pretty well from the common circular geometrical framework. How important is it that I also understand it from the hyperbolic perspective and what would I gain over my current circular understanding?

A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section of any given cone. This is not the case with hyperbolas: for a fixed cone only those hyperbolas whose asymptotes make a sufficiently small angle occur as plane sections." It...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...