1: A boat coasting through the water, experiences a resisting force proportional to v^n

The attached file is an example of a set of equations that define a gearbox composed of 4 planetary gearsets. The first 4 equations are the kinematic constraints. Where "r" indicates the size the sun or ring gear and "w" is the speed of the sun, ring, or carrier. The next 4 equations simply define new parameters (R_n) for the ratio between the size of the ring and sun gears. The last 5 equations define how these gears are connected. My question is how can I (or is it possible) to complete this worksheet in a generic way to solve for the speeds of any of the nodes in terms of some defined list of nodes and the parameterized gearbox sizes? In this example, there are 3 degrees of freedom so I might wish to solve for w[R3] (a dependent variable) in terms of w[R1], w[S2], w[S4] (independent variables), and all the parameters. The generic part comes from needing to be able to change the last 5 equations (including adding or subtracting equations) and perhaps the list of dependent and independent variables.

I have been trying to solve a larger problem (recovering data from blurred photos) and i have hit a snag. Consider an area in the plane, for example a circle with radius r=1 and centre C defined by some parametric equation, fx C=(t,0). This would give us an area A defined by (x-t)^2+y^2 <>. My aim is to construct a function f(x,y), where the value of f for any point (x,y) is equal to the range of t-values for which the point is inside the circle, with t being in the interval from 0 to T. I would really like som help in finding a method for finding f(x,y). The aim of this function would be to calculate how the image data from any single pixel would be spread over other pixels due to camera shake, with the camera shake being given by the parametric equation for C.

Hi guys, we've got a Fourier transform problem here. This is how we calculate Fourier coefficient: 4/pi*int(cos(3*x)*cos(n*x), x=0..Pi/2) (we try to expand cos(3*x)) so here we got the answer 12*cos((1/2)*Pi*n)/(Pi*(-9+n^2)) correcr answer, you see, is B3=1; but when we write this: 4/pi*int(cos(3*x)*cos(n*x), x=0..(1/2)*Pi)assuming n=3 the result shown is zero. we don't know how it works. because this value is evaluating correctly: 4/Pi*int(cos(3*x)*cos(3*x), x=0..(1/2)*Pi) the answer is right - 1.

I'm pretty new here, in maple and I think I'm not very good in math too but I would like to discover how to limit or set the domain of my x. Example: sin(x); I would like to set the type of the x to N (natural) and the type resulting to R (real). But after hours and hours of searches on google I subscribed to ask this to you, gentlemen :P Thank you everyone

Hi, I am interested in making the assumption T[0]<><><><><>

Bonjour, Je voudrais modéliser le vol d'une fusée à eau sous maple 11, je n sais pas par ou commencer. Merci d'avance pour votre aide.

Hi, I am trying to create a sheet to show the derivation of 2nd and 4th-order function derivatives as part of a 5-point finite difference scheme for a 1-D model (a continuous beam on an irregular foundation). I have isolated 2 simultaneous equations by using Taylor polynomials and would like to cast these in matrix form and then solve for each of the D-operators symbolically. Is there a simple way to do this or do I have to work with the ops manually? thanks for any help, Neil

I have difficulties understanding why exactly Maple finds the question difficult to answer. First attempt: assume(a>0); a:=sqrt(b^2); eval(a, b=2); (1/2) / 2\ a := \b / (1/2) 4 I suppose the problem is that after the assignment Maple forgets the assumption a>0(?). Is there a way to make _real_ assumptions on variables, which Maple will not forget and possibly warn me if I try to violate?

Dear All, I have two odes, dX/dt = -X(t)*Y(t) and dY(t)/dt = X(t)*Y(t) I can solve these numerically using the following code: eq_1:=diff(X(t), t)=-X(t)*Y(t); eq_2:=diff(Y(t),t)=X(t)*Y(t); IC:={eq_1, eq_2,X(0)=10,Y(0)=1}; F:=dsolve(IC, {X(t),Y(t)},type=numeric, method=rosenbrock); h := theta->eval(X(t),F(theta)); h(1); However, I would like to add perturbations at specific time points. For example, at t=10, set X=5, or at t=15, Y=0. How should I do this in maple? Note: my actual situation involves a 100 odes. Thanks, Colin

How can I write a recursive algorithm on maple wich gives me the fibonacci polinomies knowing that: F1(x) = 1 F2(x) = x Fn+1(x) = xFn(x) + Fn−1(x), n = 2, 3, ... i think it's easy but still can't do it...if anyone knows help me please

I subs (a^2=4b, expression) and get (1+b)*x^2+a*(1+b)*x+b(b-1)+2*b visually, (b+1) is a factor of the polynomial but the machine refuse to recognise this, I tried /(b+1), collect, expand and simplify and all failed. This is quite a frustration to new user who just want to get things done quickly!

Hello, everyone! Given a polynomial: f := x^2*y + 10*z*w + 2*a*t I would like to know how many different variables appear in f. Is there a command I can use to do this? My actual polynomial is more like: f := x[1]^2*x[2] + x[127]*x[3] + ... Any help would be appreciated! Thank you very much, and happy holidays! Best, Susan

I am new to the Maple v.11 world and trying to figure out how to do things. I'm getting lost with the instructions in the help screens. Here is the problem: Can somebody show me how to enter this into Maple. Find the probability of an observation falling within one standard deviation of the mean. A Poisson distribution with [lambda]=16. Two other questions are normal distribution with mean=20, and a gamma distribution with [alpha]=4 and [theta]=5. I'm sure that if I can figure out one of the problems, I can figure out the others. Somebody please show me how to enter the problem

Hi I have data I want to fit it I do not know the model function I know only that the relation between X and Y is non-linear and there is six parameters I want to know their values from the fitting.can I do this using Maple or it is impossible. this is Maple work sheet: Download 7089_X0165.txt
View file details this is the input data: Download 7089_Nonlinearfit.mws
View file details