Cylindrical Polar Coordinates

Related BrainMass Solutions

• Cylindrical polar coordinates

  47447 Cylindrical Polar Coordinates Express the potential function U in cylindrical polar coordinates..

• Laplacian of a function under different coordinates

  (a) Calculate the Laplacian of function u(x,y,z) = x^3 - 3xy^2 + z^2 in 3D Cartesian coordinates. (b) Convert the formula for u into formula for u involving cylindrical polar coordinates. Then compute the Laplacian using the cylindrical polar form.

• Calculation of volume by integration

  volume of Q can be calculated by For the sphere of (assume ) The polar angle is measured down from the z axis, so So the volume of sphere is (c) Using the spherical coordinates, the volume of the sphere is Supplemented with diagrams

• position of the center of mass of a thin parabolical shell

  The cylindrical polar coordinates are used to determine the position of the center of mass of a thin parabolic shell.

• Use Polar Coordinates to Find the Volume of a Ring-Shaped Solid

  36520 Use Polar Coordinates to Find the Volume of a Ring-Shaped Solid A cylindrical drill with radius 2 is used to bore a hole throught the center of a sphere of radius 7.

• Intersection of surfaces

  When we have a cylindrical symmetry it is useful to use polar cylindrical coordinates: (1.2) Where is the distance from the origin and is the angle between the radius vector to the point and the positive x-axis measured counterclockwise.

• Center of mass of cone, cylindrical coordinate system

  The element of volume in cylindrical coordinates is dV=r dr d theta dz, where theta is the polar angle, r is the polar radius (r=(x^2+y^2)^(1/2) for a point (x,y,z) in space) and z is the hight from the xy-plane. b.

• Absolute maximum and the absolute minimum, derivatives and logarithmic differentiation.

  Let Q be the sphere: X^2 + Y^2 + Z^2 = a^2 a) Use CYLINDRICAL coordinates to set up the integral to calculate the volume of Q b) Use SPHERICAL coordinates to set up the integral to calculate the volume of Q c) Solve for Q using either a or

• Laplace equation in cylindrical coordinates

  Check out the following site: http://mathworld.wolfram.com/HelmholtzDifferentialEquationCircularCylindricalCoordinates.html For a nice solution of the Helmholtz equation in cylindrical coordinates.