Circular Movement: Exploring Particle Motion

[peripatein]

Hello,

If the position of a particle w.r.t time is given as X=Acos(t)exp(-at), and Y=Asin(t)exp(-at), then it is pretty clear that the particle is moving in concentric circles around the origin with decreasing radius. Is anything else ought to be stated in order to describe the motion of the particle? I mean, does it suffice, when asked to describe the motion of this particle, to simply state that its motion would be as I delineated above? In other words, what more can one learn, and say, about the particle's type of movement?

Also, I have found that dx/dy = [y+a√(A^2exp(-2at) - y^2)] / [ay - √(A^2exp(-2at) - y^2)]. Is that correct and, if so, can it be further simplified?

 

[AJ Bentley]

Not concentric circles really - can you think of a better word?

 

[peripatein]

Spiral?

 

[AJ Bentley]

What kind of spiral?

 

[peripatein]

Converging to the origin?

 

[AJ Bentley]

http://www.mathwords.com/s/spiral.htm

 

[peripatein]

Logarithmic spiral, then? Would that suffice as an answer, or ought it to be shown mathematically, explicitly via the equations?

 

[AJ Bentley]

Logarithmic spiral, then? Would that suffice as an answer, or ought it to be shown mathematically, explicitly via the equations?

Under the drawing in Mathworlds, there's a formula given.
Can you derive it (or something very similar) from your equation?

 

[peripatein]

Thanks! :-)