Find the components of vectors in polar coordinates when their components in Cartesian coordinates are $ x, y $ and $ \dot{x}, \dot{y} $ respectively.

Question

Accepted Answer

সঠিক উত্তর: । ব্যাখ্যা:

Component	Polar Coordinate	Formula
Position	r (radial distance)	\(r = \sqrt{x^2 + y^2}\)
	θ (polar angle)	\(θ = \arctan(\frac{y}{x})\)
Velocity	ṙ (radial velocity)	\(ṙ = \frac{x\dot{x} + y\dot{y}}{r}\)
	rθ̇ (transverse velocity)	\(r\dot{θ} = \frac{x\dot{y} - y\dot{x}}{r}\)

Find the components of vectors in polar coordinates when their components in Cartesian coordinates are \\( x, y \\) and \\( \\dot{x}, \\dot{y} \\) respectively.