Conditions Definition and 978 Threads

Hello, What could be wrong when the total inertia matrix of a robotic manipulator is non invertible when under certain values of the joint angles? Thank you

Homework Statement Use Friedmann equations to show that if ##\dot{a} > 0##, ##k<0## and ##\rho>0## then there exists a ##t*## in the past where ##a(t*)=0## Homework Equations [/B] Friedmann : ##(\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{k}{a^2}##The Attempt at a Solution [/B]...

Homework Statement Homework Equations $$\frac{dy}{dx}=f(x)~\rightarrow~dy=f(x)dx~\rightarrow~y=\int f(x)dx$$ $$F=ma,~a=\frac{dv}{dt}$$ The Attempt at a Solution $$-\frac{mgR}{s^2}=mv\left( \frac{dv}{ds} \right)\rightarrow~v^2=\frac{2gR}{s}+C$$ $$v_0(s=R)=\sqrt{2gR}\rightarrow~C=2g(R-1)$$...

Homework Statement Find an equation of the plane that passes through the point (1,2,-2) and that contains the line x=2t,y=3-t,z=1+3t. Homework EquationsThe Attempt at a Solution I know that a plane is determined by a base vector and a normal vector, and the equation of the plane is ##\vec{n}...

Homework Statement Let f : R → Rn be a smooth function. Give necessary and sufficient conditions on f so that the antiderivative F(x) = ∫f(t)dt (from 0 to x) is periodic with period p ≠ 0 Homework EquationsThe Attempt at a Solution My initial thought is that as long as f is periodic then F...

Homework Statement Hello, For two waves to be coherent, they must have the same frequency right? Does this on its own implies a constant phase different between any point on one wave and any on the other. So, for example, if we had two waves with different wavelengths and velocities but equal...

Homework Statement In a lab experiment we ran the simulation of 3 different flight conditions into a program that produced graphs of the oscillations in them conditions and we have to do a comparison of the SPO (short period oscillations) characteristics for the 3 flight conditions which are...

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

http://imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

Homework Statement Ive looked through several published journals online trying to find an experiment that I can use as background research for my report, something I can compare my findings to but I am just wasting lots of time that I could be doing the rest of my report so what I am trying to...

Whittaker (1st Edition, 1902) P.132, gives two proofs of Fourier's theorem, assuming Dirichlet's conditions. One proof is Dirichlet's proof, which involves directly summing the partial sums, is found in many books. The other proof is an absolutely stunning proof of Fourier's theorem in terms of...

Homework Statement Two lossy homogeneous dielectric media with dielectric constans ϵrl = 2, ϵr2 = 3 and conductivities a1= 15 (mS), σ2 = 10 (ms) are in contact at the z = 0 plane. in the Z>0 region a uniform electric field E1 = 20i - 50k exists (i and k being unit vectors in the x and z...

Homework Statement Deriving an s-domain equation for the following inputs a) &b) The Attempt at a Solution I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)

Working through a paper about whose rigor I have my doubts, but I am always glad to be corrected. In the paper I find the following: "We now investigate the random variable q. There are the following restrictions on q: 1) The variable q must characterize a stochastic process in the test...

I've been trying to come up with wave equations to describe the motion on vibrating rectangular (more specifically, square) membranes. However, most paper I find assume fixed edges. What are the boundary conditions I need to apply to the 2D wave equations in order to have an free boundary in a...

I have a couple homework questions, and I'm getting caught up in boundary applications. For the first one, I have y'' - 4y' + 3y = f(x) and I need to find the Green's function. I also have the boundary conditions y(x)=y'(0)=0. Is this possible? Wouldn't y(x)=0 be of the form of a solution...

Homework Statement Consider the following problems In #2, they start the solution by saying: r(t)=u(t-1) in #3, they start by saying that r(t)=t-tu(t-1) I understand how to solve the problem once you get r(t), I just don't understand how they decide what r(t) is going to be.

Homework Statement I am trying to solve a system of 2 ordinary differential equations using matlab. However, I am not able to get numerical solutions from the code despite having keyed in all possible solutions. Homework Equations The equations I am given are: dx/dt=A(x/t)+By...

I am facing some difficulties solving one of the questions we had in our previous exam. I am sorry for the bad translation , I hope this is clear. In each section, find all approppriate matrices 2x2 (if exists) , which implementing the given conditions: is an eigenvector of A with eigenvalue...

Homework Statement If ##a_n## counts the number of ways to climb a flight of n stairs if one can take 1, 2, or 3 steps at a time, then ##a_n = a_{n-1} + a_{n-2} + a_{n-3}##. What are the three initial conditions? Homework EquationsThe Attempt at a Solution I would say that ##a_0 = 1## since...

Ideal gas behavior condition is high temperature and low pressure, right? so is the book's answer to 10(a) ii wrong? https://scontent-kul1-1.xx.fbcdn.net/v/t34.0-12/14996536_1455768127770250_1228715611_n.jpg?oh=750e2555f8229aa9a4eeb17e3e80b1fb&oe=5829A2EE...

I'm trying to solve some statistical mechanics. This problem appeared. ##\frac{f\left(0\right)}{f\left(a\right)}f\left(x+a\right)=f\left(x\right)## Any idea as to which function will satisfy this equation?

The difference between Planck's Law and the Rayleigh-Jeans' Law is, in Rayleigh Jeans, the average energy per mode is ##kT##, whereas in Planck, it is ##\frac{hc}{λ(e^\frac{hc}{λkT}-1)}##. These average energy formulas are multiplied by another formula to give either Planck's Law or the...

Three conditions must be met in order for the Poisson Distribution to be used: 1) The average count rate is constant over time 2) The counts occurring are independent 3) The probability of 2 or more counts occurring in the interval $n$ is zero Simply, why must these conditions be met for valid...

So I am studying conditionals in proposition logic, and I have discovered that there are a variety of ways to phrase a conditional "if p, then q" in English. Some of the harder ones are... p is sufficient for q a necessary condition for p is q q unless ~p (where ~ is the not operator) p only...

When dealing with heat transfer, there are cases where Q can be expressed by C*ΔT, for some proportionality constant C. However, in isothermal processes for example, this formula would lead to a mistake, for any value of C (because it would imply Q=0, which is not true generally speaking). What...

So this is kind of a speculative question but it is something I have long wondered about. I know that if I were to suddenly find myself transported backward in time, say 5000 years, or transported to a primitive Earth like planet, chances are that I would probably die in no time at all. I...

Hello, I have some sort of problem which I would like to explore. We have yet to touch it in the class in the university, but it seemed like a crazy idea when i stumbled upon it. Let there be a very long pipe with an inner radius of 1.08 meters and outer radius of 1.1 meters. The material of...

Hi all! I have to calculate the natural frequency of the system. Any idea of boundary conditions of this case? There is beam supported by two springs on the left side.

I'm facing some difficulties in using "boundary conditions" in a simple wavefunction. The wavefunction I'm considering is $$\xi(x,t)=A sin (k x \pm \omega t +\psi)$$ The minus or plus are for progressive or regressive waves. The indipendent parameters are 4: ##A##, ##k##, ##\omega##, ##\psi##...

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

I am working in ℂ3 in this question. (If it will make it easier, we can work in a bounded subspace.) Suppose you have, in each of the three complex planes whose Cartesian product make up the space in question, a set of points. (You do not have knowledge of generators of these sets, or whether...

Hi there, I'm trying to simulate a vibrating plate with free edges. If i consider a consider a plate with fixed edges, the eigenvectors of the matrix bellow (which repesents the Laplacien operator) with S as a nxn tridiagonal matrix with -4 on the diagonal and 1s on either side (making the...

In calculus of variations, extremizing functionals is usually done with Dirichlet boundary conditions. But how will the calculations go on if Neumann boundary conditions are given? Can someone give a reference where this is discussed thoroughly? I searched but found nothing! Thanks

The Schwarzschild equation of motion, where coordinate length is differentiated by proper time is as far as I know r''(t) = -\frac{G\cdot M}{r(t)^2} + r(t)\cdot{\theta}'(t)^2 - \frac{3\cdot G\cdot M\cdot{\theta}'(t)^2}{c^2} {\theta}''(t) = -2\cdot r'(t)/r(t)\cdot{\theta}'(t) Now the question...

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] I know dV=1/C∫idt and that we integrate the voltage from V to V0. What I don't get are the boundary conditions for t - How do we get what we get in the parenthesis? My closest assumption is that the t/T values refer to the...

I'd like to read some articles, papers, or whatever scientific there is about the prospects and impacts of climate change for professional ground based astronomy and observatory sites. In particular, which locations which are now among the most suitable sites for observatories - especially...

Suppose we are solving a diffusion equation. ##\frac{\partial}{\partial t} T = k\frac{\partial^2}{\partial x^2} T## On the domain ##0 < x < L## Subject to the conditions ##T(x,0) = f(x) ## and ##T = 0 ## at the end points. My question is: Suppose we solve this with some integration scheme...

For the case of a particle attached to an inextensible string which is hanging at rest and then provided an impulse horizontally, what conditions must the system meet in order to allow for COMPLETE circular motion. I am well aware the tension at the apex of the motion must be satisfy one of the...

If I am doing a simple, static analysis on something like a table, or tripod with a vertical force acting on it, what support condition do I assign to the base at which the legs contact the ground? I feel like it is incorrect to specify this as "fixed," since that would be like saying the legs...

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...

Mathematically, what conditions must a B-field that obeys the Biot-Savart Law satisfy before it will obey Ampere's Law? Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

Homework Statement Find the Green's function $G(t,\tau)$ that satisfies $$\frac{\text{d}^2G(t,\tau)}{\text{d}t^2}+\alpha\frac{\text{d}G(t,\tau)}{\text{d}t}=\delta(t-\tau)$$ under the boundary conditions $$G(0,\tau)=0~~~\text{ and }~~~\frac{\text{d}G(t,\tau)}{\text{d}t}=0\big|_{t=0}$$ Then...

Homework Statement Derive the basic relationship that the Antoine equation represents. Most importantly, explain the underlying condition when the Antoine equation applies and the underlying assumptions for the Antoine equation to be valid. Homework Equations Clausius-Clapeyron Equation...

The equation is Uxx + Uyy = 0 And domain of solution is 0 < x < a, 0 < y < b Boundary conditions: Ux(0,y) = Ux(a,y) = 0 U(x,0) = 1 U(x,b) = 2 What I've done is that I did separation of variables: U(x,y)=X(x)Y(y) Plugging into the equation gives: X''Y + XY'' = 0 Rearranging: X''/X = -Y''/Y = k...

In various explanations of the event horizon which do not invoke the existence of a firewall (thereby upholding the dictum that an observer would not notice any difference upon passing the event horizon until she looked out the window), one uses the concept of a theoretical observer passing the...

Hello, I want to know if there exist any result in literature that answers my question: Under which conditions on the real valued matrix ## R ## (symmetric positive definite), the first argument results in and guarantees the second one: 1) for real valued matrices ##A, B, C,## and ## D ## with...

Homework Statement I want to find conditions over A,B,C,D to observe a stable limit cycle in the following system: \frac{dx}{dt} = x \; (A-B y) \hspace{1cm} \frac{dy}{dt} = -y \; (C-D x) Homework Equations Setting dx/dt=0 and dy/dt=0 you can find that (C/D , A/B) is a fixpoint. The Attempt...

Hello! (Wave) Does it suffice to show that the triple product is 0? If we show that $a \cdot (b \times c)=0$ we will have that $a$ is orthogonal to $b \times c$. $b \times c$ is orthogonal to both $b$ and $c$, so we will have that $a$ will be parallel to $b$ and $c$. Right? But why does...

Hello, I am curious as to how one appropriately matches an interior and exterior solution in GR, i.e. where the interior corresponds to the field of some finite spherical mass (perfect fluid sphere, for the Schwarzschild interior solution). Specifically, looking at both the Schwarzschild...