{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

l_notes17

# l_notes17 - Lecture XVII Curvilinear Coordinates Change of...

This preview shows pages 1–2. Sign up to view the full content.

Lecture XVII Curvilinear Coordinates; Change of Variables As we saw in lecture 16, in E 2 we can use the polar coordinates system. In this system, we have a fixed point O and a fixed ray Ox . The coordinates of a point P are given by r , the distance from P to O , and θ the angle made by Ox to OP . We can OP and Ox , as measured going counterclockwise from change the system of coordiantes from polar to Cartesian through a system of equations: x = r cos θ, y = r sin θ. This is called the defining system . To go from the Cartesian system to the polar one, we use the inverse defining system : r = x 2 + y 2 , θ = arctan y , x for ( x, y ) in the first quadrant. Generally, we can introduce new non-Cartesian coordinates u, v by writing x, y as functions of these new coordiantes: x = g ( u, v ) , y = h ( u, v ) . These equations form the defining system for the new coordiantes. They can be summarized by writting the position vector ˆ j. R ( u, v ) = x ˆ i + yj = g ( u, v ) ˆ i + h ( u, v ) ˆ In working with curvilinear coordinates, it is useful

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}