Chain Definition and 939 Threads

I have a three link revolute manipulator at the origin. I know all the link lengths. The joint angle for the third link is coupled to the second such that Theta3 = k*Theta2. I want to determine the joint angles (thetas) of the manipulator given that the third link should lie on a line an angle...

Homework Statement A chain of length L and mass density σ kg/m is held in a heap. I grab an end of the chain that protrudes a bit out of the top. The heap is then released so that the chain can unravel with time. Assuming that the chain has no friction with itself, so that the remaining part...

Suppose I have F(x,y) and y=y(t) and x=x(t) Therefore, Ft = Fx*xt + Fy*yt. Right? Can I write Ftt = (Fxx*xt + Fyy*yt)*xt + Fx*xtt + (Fxx*xt + Fyy*yt)*yt + Fy*ytt ? Basically I'm trying to figure out the second derivative by chain rule.

I am designing a bike in Autodesk Inventor for a university project, and I am stuck with the sprockets. Inventor can create them fairly easily when you know the norm of the sprocket and the number of teeth it has, but I don't know the standard of the sprocket I have to design; I merely know that...

If a function is given by u = u(T,v) how to use the chain rule to write how u changes with respect to T & v. Please specify the steps involved. i understand chain rule as [SIZE="4"]\frac{du}{dx} = \frac{du}{dy} \frac{dy}{dx}

Homework Statement If Z= F(x-y), show that Zx + Zy = 0 Homework Equations The Attempt at a Solution Suppose I let Q = x-y. Then, by chain rule, Fx(Q) * 1 + Fy(Q) * -1. By identity, this statement must hold for all values x,y. In particular, it must hold for x=y. By x=y...

Homework Statement So there is an exercise in which I should "verify" the chain rule for some functions. In other words to do it by substitution, then doing by the formula and checking if the results are the same. (and checking with the book`s answer too) For a few of them, they just don`t...

Homework Statement A chain of atoms are connected by identical springs of force constant k. Suppose teh atoms of mass m alternate with atoms of mass M. Thus the crystal consists of a sequence ... MkmkMkmMkmk ... which is the periodic repetition of unit cells Mkmk. The size of the unit cell is...

I was wondering how to prove the multivariable chain rule \frac{\mbox{d}z}{\mbox{d}t}=\frac{\partial z}{\partial y}\frac{\mbox{d}y}{\mbox{d}t}+\frac{\partial z}{\partial x}\frac{\mbox{d}x}{\mbox{d}t} where z=z(x(t),y(t)) I don't really need an extremely rigorous proof, but a slightly...

Critical mass is over 50kg so let's say I have 2 halves of a sphere of the isotope U-235, each weighing 30 kg. I drop one onto the other so that they form a supercritical sphere. No doubt a chain reaction would begin, but I assume it would produce energy on the level of a nuclear reactor rather...

Homework Statement A linear chain consists of N identical particles of mass m are connected by N+1 identical, massless springs with force constant k. The endpoints are fixed to walls on each side. In the static configuration each spring is stretched from its relaxed length l0 to a new length...

Homework Statement w= f(x,y) x = u + v Verify that Wxx - Wyy = Wuv y = u - v Homework Equations The Attempt at a Solution I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...

I was doing my homework and I ran into a problem of a chain rule within a chain rule. When do I know what to assign a value? For example: y=e^{-x^2} When I assign u=e^{-x} and y=u^2 I get a wrong value. According to cramster I was supposed to assign y = e^u and u=-x^2. But when am I supposed...

Hi there, My equation to solve is (xy+(x^2))dx + (-1)dy=0 For method of exact solutions, the partials are not equal to each other so I cannot use exact solutions (reverse chain rule) I don't know how to solve this

Homework Statement Find the derivative of the following: Homework Equations Y= x^3(5x-1)^4 The Attempt at a Solution 4(3x^2(5x-1)^3)(4(3x^2(3(5x-1)^2)(2(5x-1)(5)

Just some general questions as I'm confused with when to use chain rule when not to. For instance, to find the derivative of e^sqrt(x), the right answer is to use chain rule to get e^sqrtx*the derivative of sqrt(x). BUT, isn't there a formula that: d/dx K^x = In(K)*K^x? K for constant and x...

This is probably a noob question, background in probability theory isn't great but I was shown this problem in a lecture: "Suppose a gambler starts out with £n, and makes a series of £1 bets against the house. Let the probability of winning each bet be p, and of loosing be q = 1 − p. If...

Homework Statement Calculate ∂f/∂s + ∂f/∂t at s = 2, t = -1. Given: f = f(x,y) x = s - t y = s2 + t2 ∂f/∂x (3,5) = 0.06170 ∂f/∂y (3,5) = 0.06170 Homework Equations ∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s ∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t The Attempt at a Solution...

I did a derivative problem, but my book says that my answer is wrong. f(x)=x2(x-2)4 I didn't see much use in the chain rule so I used the product rule. x2(4(x-2)3) + (x-2)4(2x) =4x2(x-2)3 + 2x(x-2)4 The book says that instead of this, the answer is ... x2(4(x-2)3(1)) + (x-2)4(2x) =...

Homework Statement http://images.calcchat.com/solutionart/etf5e/03/d/se03d01063.png Homework Equations The Attempt at a Solution I get to the third row, but can't simplify (Sin2θ)(Cos2θ). I'm looking at the trigonometric double angle formulas, and still can't figure out how the...

A chain consisting of five links, each of mass 0.1 kg, is lifted vertically with a constant acceleration of a = 2.5 m/s2. Find the magnitude of (a)the force on link 1 from link 2 (b)the force on link 2 from link 3 (c)the force on link 3 from link 4 (d)the force on link 4 from link 5...

Homework Statement Suppose f(x,y) = 2x^5 + 4xy + 2y^3 g1(u,v) = u^2 - v^2 g2(u,v) = uv h(u,v) = f(g1(u,v), g2(u,v)) Use chain rule to calculate: dh/du (1,-1) and dh/dv (1,-1) Homework Equations The Attempt at a Solution i let h (u,v) = 2(u^2 - v^2)^5 + 4(u^2-v^2)(uv) +...

For some reason I am struggling with these problems. I am lost as a goose trying to fly south for the winter! Homework Statement 9^(5-x2) and another derivative problem using chain rule r/square root of the whole term r^2+5 Homework Equations 1st equation= d/dx= a^x ln a 2nd...

Homework Statement cot^2(Cos\theta)Homework Equations chain rule f prime (x) = f prime(g(x) * g prime (x) The Attempt at a Solution I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat...

I always get muddled when I'm dealing with chain rule of any degree of complexity and also when dealing with powers of trig. functions - this problem contains both: find \frac{\partial n}{\partial A} and \frac{\partial n}{\partial D} of the following function...

I'm curious if there's a chain rule for the commutator (I'll explain what I mean) just like there's a product rule ([AB,C]). So, say you have an operator, which can be expressed in terms of another operator, and we know the commutation relationship between x and another operator, y. I'll call...

Suppose X is a random walk with probability P(X_k=+1)=p and P(X_k=-1)=q=1-p and S_n=X_1+X_2+...+X_n Can anyone explain why does line 3 equal to line 4? P(S_k-S_0≠0 ,S_k-S_1≠0 ,…,S_k-S_{k-1}≠0) =P(X_k+X_{k-1}+⋯+X_1≠0 ,X_k+X_{k-1}+⋯+X_2≠0 ,…,X_k≠0) =P( X_k≠0 ,X_k+X_{k-1}≠0...

Homework Statement For the van der Waals equation of state, confirm the following property: (∂P/∂T)V (∂T/∂V)P (∂V/∂P)T = -1 Homework Equations The van der Waals equation of state is: P = nRT/(v-nb) - an2/V2 *R, n, a, b are const. The Attempt at a Solution I...

It's been years since I've done maths properly so I'm rusty with it. I'm helping out a colleague at work who is studying maths for an OU course. Homework Statement Part 1: Differentiate function. f(x) = e^(0.5x+cos(x)) Part 2: Use answer from part 1 to show. g(x) =...

Solve the following: d/dt cos(theta) d/dt t sin(theta) d/dt r cos (theta) d/dt r^2 (theta) d/dt e^ (-3x) d/dt (x^2 + y^2) I would assume all by the second one are 0 since your solving for terms dt and not theta, x, y, or r... I don't think its right at all. I know it goes something...

Hi, Say x=position, v=velocity, a=acceleration, t=time. Thanks! EDIT: I just realized that 2/x is not a constant and thus I shouldn't have treated it as a constant (taking the derivative of it as 0). However, I don't understand how to take the derivative with respect to t of it.

I want to find the second order derivative for f(x,y),x(u,v),y(u,v), f depends on x and y, and x and y depends on u and v. I'm trying to find \frac{{\partial^2 f}}{{\partial v \partial u}}This is what I did: \frac{{\partial f}}{{\partial u}}=\frac{{\partial f}}{{\partial x}}\frac{{\partial...

I'm confident in my math ability, but how is it that by using the chain rule... W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dt} dx can be turned into W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dx} \frac{dx}{dt} dx = \int^{v_2}_{v_1}mv dv ? I understand the...

From james stewart calculus Early Transcendentals.Before he states the proof he intoduced a property of differentiable funcion My problem is how we defined \epsilon to be 0 when \Delta x=0 where this is not in the Domain.

Is there an elegant and simple proof of the Chain Rule? Every proof I've found is complex and mind-boggling

Hi, I have been searching the internet for some gentle introductions of Fibonacci chain, but so far I haven't found anything. I wonder if anyone can recommend some good introductions to me, e.g. a book, an article... Thank you.

Let X be a non-empty set, and let S contain all countable subsets of X. Partially order S by inclusion. Let C be a totally ordered subset ("chain") of S, and let U = \cup_{E \in C} E It appears that U is not always countable: if it were, U would be an upper bound of the chain C, and U would...

Homework Statement Use the chain rule, the derivative formula Dxsinu=cosuDxu, together with the identities cosx=sin(\pi/2 -x) and sinx=cos(\pi/2 -x) to obtain the fomula for Dxcosx. Homework Equations Chain rule: dy/dx=dy/du\cdotdu/dx The Attempt at a Solution For my second...

I have a state transition probability matrix and a state probability vector [0.9 0.1; 0.1 0.9] & [0.4 0.6] respectively. Now, I want to generate the states of 1 and 0 according to this. say 100 state sequence. Any sort of help would be appreciated. Thanks.

In a Markov chain, show that a state i is persistent if and only if the mean number of visits to the state i is infinite given the chain started in state i. I thought about looking at the mean recurrence time, but that's all I have so far.

Let X be a Markov chain with a state s that is absorbing, i.e. pss(1) = 1. All other states communicate with s i.e. i → s for all states i ∈ S. Show that all states in S except s are transient. I understand this intuitively, but I'm not really sure how to start the proof.

I have learned that the primers in PCR are added to the DNA in the annealing phase, but what exactly do these primers do to the DNA? Thank you

Homework Statement A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time. (Hint...

Can anyone explain the mechanics of a chain hoist and its mechanical advantage, in mathematical terms,? thank you Bashyam

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

* I have already posted this in the General Math, but I guess the problem is more like a linear algebra problem. Currently I am using a rather simple way, to solve vector w from (M-I)w=0 (replace one equation by w1+w2+...wn=1). Is there any faster way to do this? Thank you.

From this day , if we take in account . How much population will be my following generation at the end of 2000 years(from this day). My question is , will the population be thousands or millions? Will it likely be fade away in the middle and no trace remains in the end? Any...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 The Attempt at a Solution i have no idea! question though, do the partial derivitives have to be solved and expanded then just show that one side equals the other or can...

Homework Statement \frac{d}{dx}(x+(x+sin^2(x))^3)^4 Homework Equations Calc up to Chain Rule. The Attempt at a Solution Using product and chain rule I got: \frac{dy}{dx}=4(x+(x+sin^2(x))^3)^3(1+3(x+sin^2(x))^2)(1+\frac{d}{dx}sin^2(x)) Then I calculated the derivative of sin^2(x)...

Homework Statement I have proven in two ways (correctly) that the derivative of ln|x| = 1/x (note absolute value does vanish) Now I open my textbook and see a general rule that \frac{d}{dx} ln (u) = \frac{u'}{u} And the not so general derivative of |x| is \frac{d}{dx} |x| =...