You have x(t), y(t), z(t).
Velocity vector v = (dx/dt,dy/dt,dz/dt).
Acceleration vector a=dv/dt = .
v direction tangential to the curve.
Find vector = v/|v| |n|=1 tangential to the curve.
Tangential acceleration
Normal acceleration
.
Hi guys,
I have a 3D curve that is defined by a parameterization in the form of x(t), y(t), and z(t). In the context of the problem the curve is a waterslide and I need to calculate the normal acceleration at various points along the curve. I can calculate the velocity at any point by a simple conservation of energy from the top of the slide to the point of interest, but what do I need to do to calculate normal acceleration?
You have x(t), y(t), z(t).
Velocity vector v = (dx/dt,dy/dt,dz/dt).
Acceleration vector a=dv/dt = .
v direction tangential to the curve.
Find vector = v/|v| |n|=1 tangential to the curve.
Tangential acceleration
Normal acceleration
.
Thank you for helping, but I must admit that I do not totally get it yet. Perhaps someone could help me with a simple example and then I will be able to apply it to my more complicated problem.
Imagine that my curve is defined by the simple parametrization:
x(t)=sin(t)
y(t)=cos(t)
z(t)=.01t
I am interested in the point where t=90 degrees, which represents one specific point on the curve. Based on the conservation of energy and the height at that point, I know that the rider will be traveling at 10m/s. How do I calculate his normal acceleration?