lect_07 - Total Differentiation of a Vector in a Rotating...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Total Differentiation of a Vector in a Rotating Frame of Reference • Before we can write Newton’s second law of motion for a reference frame rotating with the earth, we need to develop a relationship between the total derivative of a vector in an inertial reference frame and the corresponding derivative in a rotating system. k ˆ A j ˆ A i ˆ A A z y x + + = r in an inertial frame of reference, and k ˆ A j ˆ A i ˆ A A z y x + + = r in a rotating frame of reference. Let be an arbitrary vector with Cartesian components A r k ˆ A j ˆ A i ˆ A A z y x + + = r in an inertial frame of reference, then If + + + + + = dt dA k dt k d A dt dA j dt j d A dt dA i dt i d A dt A d z z y y x x ˆ ˆ ˆ ˆ ˆ ˆ r Since the coordinate axes are in an inertial frame of reference, 0 ˆ ˆ ˆ = = = dt k d dt j d dt i d + + + + + = dt dA k dt k d A dt dA j dt j d A dt dA i dt i d A dt A d z z y y x x ˆ ˆ ˆ ˆ ˆ ˆ r k dt dA j dt dA i dt dA dt A d z y x ˆ ˆ ˆ + + = r (Eq. 1)
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 k A j A i A A z y x + + = ˆ ˆ ˆ r in a rotating frame of reference, then If
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.

Page1 / 4

lect_07 - Total Differentiation of a Vector in a Rotating...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online