Curvilinear Definition and 87 Threads

Homework Statement A stunt car is driven off a cliff with a speed of 110 ft/s. What is the gravitational acceleration of the car normal to its path after falling for 3 seconds? Homework Equations The kinematic equations...? I'm pretty sure that this should be done in Normal and...

Hello, I have the following problem where I have two groups of transformations R_\alpha (rotation) and S_\lambda (scaling) acting on the plane, so that the orbits of any arbitrary point x=(x0,y0) under the actions of S_\lambda and R_\alpha are known (in the former case they are straight lines...

Hi there - I'm looking for a clear and intuitive explanation of how one obtains the gradient in polar / cylindrical / curvilinear coords. I do a lot of tutoring, but am finding that the method I've been using (basically chain rule + nature of directional derivative) just doesn't roll with...

Homework Statement With \vec{L} = -i\vec{r} x \nabla, verify the operator identities \nabla = \hat{r}\frac{\partial }{\partial \vec{r}}-i\frac{\vec{r}\times\vec{L}}{r^{2}} and \vec{r} \bigtriangledown ^2 - \bigtriangledown (1+\vec{r}\frac{\partial }{\partial \vec{r}})=i\bigtriangledown \times...

curvilinear coordinate systems and "periodic" coordinates Hello, we can consider a generic system of curvilinear coordinates in the 2d plane: \rho = \rho(x,y) \tau = \tau(x,y) Sometimes, it can happen that one of the coordinates, say \tau, represents an angle, and so it is "periodic"...

Homework Statement [PLAIN]http://a4.sphotos.ak.fbcdn.net/hphotos-ak-ash4/s720x720/300201_1919471514513_1473790586_31632884_1692676_n.jpg Homework Equations aR = \ddot{R} - R\dot{\phi}2 - R\dot{\theta}2cos2(\phi) a\theta = \frac{cos(\phi)}{R}\frac{d}{dt}(R2\dot{\theta}) -...

Just a quick little question. I was reading a wikipedia article about curvilinear coordinates, as well as some others, and a question popped into my head. Although we take this for granted (at least I do), now I have to ask this. From what I've seen as an engineer, we always define...

pls see the attachment. so pretty much magnitude of acc would be root (at2 + an2). i figured out an by subbing it into v2/p. but i can't figure out how to calculate at! id really appreciate the help, I've been at it for 3 hours now! thanks!

Homework Statement Drawing a field plot (using curvilinear squares) between a small sphere within a larger sphere, indicating lines of force and equipotentials. I've been trying to find a software solution to draw the diagram perfectly, but haven't had any luck in finding one. I think it...

Homework Statement A particle travels along the path y^2 = 4x with a constant speed of v = 4 m/s. Determine the x and y components of the particle's velocity and acceleration when the particle is at 4m Homework Equations 1st and 2nd derivatives?? The Attempt at a Solution not...

Homework Statement Hi. I have a doubt with this exercise. I'm not sure about what it asks me to do, when it asks me for the curvilinear integral. The exercise says: Calculate the next curvilinear integral: \displaystyle\int_{C}^{}(x^2-2xy)dx+(y^2-2xy)dy, C the arc of parabola y=x^2 which...

I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal heights for ellipsoids and another set of x, y, and z coordinates. I am so confused looking at how to convert these things. I know I need to iterate in order to go from cartesian to...

Hi All, I have been trying to understand some fluid mechanics in a research paper and have been wrestling with the mathematics for quite some time now without success. I want to derive gradient operator with following coordinate system in R^3 space Let and arbitrary curve C be locus of...

Homework Statement Diagram from picture attached R= 200 + 50sin (2pi nt), n=2 R= 200+ 50sin(4pi*t) mm ThetaDot = 120 rev/minute = 12.566 rad/s Gamma(Y) = 30 degrees Calculate acceleration when velocity is max Homework Equations ar= rDotdot - r*(thetaDot)^2 aTheta=...

If an object O is performing rectilinear motion w.r.t a Galilian body of reference K then w.r.t an accelerated body of reference K', O performs 'curvilinear' motion... What I ask for is a detailed explanation of this statement.

I wonder how Dirac equation transform under change of coordinates (in flat spacetime). Should I simply express partial derivaties of one coordinates in another or it is necessary to transform Dirac matrices as well?

Homework Statement A 750N man raises a 200N bucket of water 30m up a helicoidal staircase. If we know that the staircase has a 10 meter radius and does exactly 4 complete turns in the 30m span, what was the total work done by the man against gravity? Also, in the same scenario, what is the...

Hello, what does curvilinear abscissa mean? thank you

Hello, a system of curvilinear coordinates is usually expressed by an admissible transformation represented by a set of real scalar functions x_i=x_i(u_1,\ldots,u_n). Does it make sense to form a system of curvilinear coordinates where the [itex]x_i[/tex] and [itex]u_i[/tex] functions are...

Hello, given a system of curvilinear coordinates x_i=x_i(u_1,\ldots,u_n); u_i=u_i(x_1,\ldots,x_n) and considering the position vector \mathbf{r}=x_1\mathbf{e}_1+\ldots+x_n\mathbf{e}_n there is the well-known identity that defines the reciprocal frame: \frac{\partial \mathbf{r}}{\partial u_i...

A radar is tracking a rocket. At some instant of time, the distance, r measured as 10 mi and angle 30º. Determine the velocity and acceleration of the rocket. Velocity: v = ds/dt, Acceleration: a=dv/dt Relationship Displacement- velocity –acceleration: ads = vdv Absolute Circular Motion-...

Homework Statement A package is dropped from the plane which is flying with a constant horizontal velocity of va=150 ft/s. Determine the normal and tangential components of acceleration, and the radius of curvature of the path of motion (a) at the moment the package is released at A, (b)...

Hi, if we consider a transformation of coordinates Cartesian\rightarrowPolar, it is straightforward to derive r = (x^2 + y^2)^{1/2} and \theta = atan2(y/x), because we actually know what our new coordinate system should be like. Now let's pretend we have never seen polar coordinates, and we...

correlation, linear or curvilinear... Hello Forum, usually the Pearson coefficient is meaninful to find the linear relationship between two variables. What if the relationship is not linear? How about quadratic? I heard of the Spearman’s rank correlation coefficient, which does not depend...

Homework Statement Given, y2 = 9x3 + 6x, where x and y are in metres and y is positive. What is the normal component of the acceleration when x= 3m, \dot{x} = 7ms-1 and \ddot{x} = 8 ms-2? Homework Equations V = Vxi + Vyj Vx = \dot{x} Vy = \dot{y} a = axi + ayj ax = \ddot{x} ay =...

Homework Statement The quality assurance procedure for ball bearings has them coming down a shute and bouncing through a hole in a plate as shown. Acceptable balls pass through the hole and impact the inclined slope at Q. Find HW http://hdimage.org/images/5plyw1jdci01pyz641pb.jpg Homework...

Hi, I have a certain NON-orthogonal curvilinear coordinate system in 3D (in the metric only g_{13}=g_{23}=g_{31}=g_{32}=0) and I want to take the curl (\nabla\times\mathbf{v}) of a vector. Any idea on how to do this? The only information I can find is about taking the curl of a vector in...

Homework Statement There is a child's toy, which has the shape of a cylinder mounted on top of a hemisphere (the picture the book has looks like a half of a circle with a square on top.). The radius of the hemisphere is R and the CM of the whole toy is at a height h about the floor. (this in...

heres the diagram for the problem.. i14.photobucket.com/albums/a322/guitaristx/asdf.jpg Im just trying to find the horizontal distance the water hits the building at...the answer should be in terms of horizontal distance from point B. Heres my work...any suggestions would be great...

Hi guys,Im Chris, I am new here. I am in Dynamics doing curvilinear motion. Homework Statement A truck travels at a speed of 4m/s along a circular road with radius if 50m. For a short distance, from s=0, its speed is then increased by a(tan) = (0.05s) m/s, where s is in meters. Determine the...

Homework Statement A particle moves along the curve y(x)=x^2-4 with constant speed of 5 m/s. Determine the point on the curve where the max magnitude of acceleration occurs and compute its value. Homework Equations radius of curvature |a|=\sqrt{a_n^2+a_t^2} The Attempt at a Solution I have...

If we work in cartesian coordinates, we say for instance, that D_x \phi = \left( \frac{\partial}{\partial x} + i g \sum_a T_a A^a_x \right) \phi where g is the gauge coupling, and \{T^a\} are the generators of the gauge group, and \{A^a_\mu\} is the gauge vector field. But what happens when...

Given an orthogonal curvilinear coordinate system (q_{1},q_{2},q_{3}) with standard orthonormal basis vectors (\hat{e}_{1},\hat{e}_{2},\hat{e}_{3}), how would you prove the following?: \frac{\partial \hat{e}_{i}}{\partial q_{j}}= \hat{e}_{j}\frac{1}{h_{i}}\frac{\partial h_{j}}{\partial...

Hey guys, Here's the question: A point A moves along a curve with the equation x = y^2/6 and is elevated in the y direction at a constant velocity of 3 in/s. Calculate the velocity and the acceleration when x = 6 in. So I solved for y and y=sqrt(6*x) and when x=6 y=6. Since the...

Homework Statement When I work in general curvilinear coordinates and in particular for the computation of line and surface integrals, do I need to do anything apart from working through the 'usual steps?' Homework Equations If I am correct, computation of line and surface integrals is...

Hello, I have a "simple" problem for you guys. I am not expert in math and so try to be simple. I explain the problem by starting with one example. The polar coordinate system has the following main property: with two parameters, rho and theta, each point is described as the intersection of...

Im taking a course in contiuum mechanics and had some questions that I am sure are pretty basic but I'm not getting. We just started curvilinear coordinates and I was curious if someone could explain in a little simplier language of what the superscript and subscripts mean. Or if you...