As far as I understand, when we want to differentiate a vector field along the direction of another vector field, we need to define either further structure affine connection, or Lie derivative through flow. However, I don't understand why they are needed. If we want to differentiate ##Y## in...
1. Homework Statement
Two points in a plane have polar coordinates P1(2.500m, pie/6) and P2(3.800m, 2pie/3) .
Determine their Cartesian coordinates and the distance between them in the Cartesian coordinate system. Round the distance to a nearest centimeter.
2. Homework Equations
Ax=Acosθ...
MENTOR note: moved from General Math hence no template
What would be the Y-Axis if:
X-Axis: theta=266.4 phi=-28.94
Z-Axis: theta=192.85 phi=27.13
where:
theta=atan(Y/X)
phi=asin(Z/R)
My thinking, theta is +90 from X-Axis and phi is -90 from the Z-Axis.
Is the Y-Axis theta=356.4 phi=-62.87?
1. Homework Statement
imgur link: http://i.imgur.com/pb14Q4Q.png
2. Homework Equations
3. The Attempt at a Solution
The thing I don't understand is where the first two terms of each 2nd order ODE came about.
I understand that they are there because the coordinate system is rotating...
It can be found in any advanced calculus textbook the proof that, for a "well-behaved" space curve, the acceleration vector can be decomposed into components along the tangent and normal unit vectors. The acceleration vector is always orthogonal to the binormal vector.
The decomposition is...
1. Homework Statement
Transform the coordinates from the red c-system to the blue system. (Picture)
2. Homework Equations
Using(X Y) for the red cartesian system and (x y) for the blue system
3. The Attempt at a Solution
The solution to this problem gives
x=Xcos▼ + Ysin▼
y=-Xsin▼+Ycos▼
Im...
Suppose a position vector v is rotated anticlockwise at an angle ##\theta## about an arbitrary axis pointing in the direction of a position vector p, what is the rotation matrix R such that Rv gives the position vector after the rotation?
Suppose p = ##\begin{pmatrix}1\\1\\1\end{pmatrix}## and...
The spectral radiance of a blackbody has units of W·sr-1·m-2·Hz-1. How do I deal with these units if I want to think about a 2D problem of radiation in Cartesian coordinates? I assume that instead of a sphere of emission (which would result in artificial decrease in intensity with the inverse...