HallsofIvy said:Any helix "traces out a helical trajectory"! Do you mean a helix whose axis is a helix?
I would do it this way: first assuming the "base helix"- that is the one forming the axis of the helix we want- has the z-axis as axis, we can write it as x= R cos(t), y= R sin(t), z= ct[/itex] where "c" controls the "pitch" of the helix. Now, the hard part: Find the normal and bi-normal to that curve. Those you can use as axes to give the same parametric equations for the "real" helix you want, with, say, radius r and pitch d. The parametric equations for that helix will be the sum of the two sets of parametric equations- you get the point on the axial helix and then add the components out to the "real" helix.
Helix Tracing Helical Trajectory is a scientific method used to track the path of a particle or object that moves in a helical, or spiral, motion. It involves analyzing the position, velocity, and acceleration of the object at each point along its trajectory.
Helix Tracing Helical Trajectory is useful for understanding the motion of objects in a helical path, such as projectiles, planets, and charged particles in a magnetic field. It can also be used to calculate the forces acting on the object, and to predict its future path.
The key components of Helix Tracing Helical Trajectory are the initial position and velocity of the object, the radius of the helix, and the angular velocity of the object. These factors determine the shape and size of the helix, as well as the speed and direction of the object at any given point along its trajectory.
Helix Tracing Helical Trajectory differs from other methods, such as parabolic or circular trajectory tracking, in that it takes into account the helical path of the object. This allows for more accurate predictions of the object's future position and velocity, especially for objects with complex or non-linear motion.
Helix Tracing Helical Trajectory has many real-world applications, including in physics research, aerospace engineering, and sports science. It can be used to study the flight of projectiles, the orbit of satellites, and the motion of athletes in sports such as baseball and javelin throwing. It is also used in medical imaging, such as in MRI machines, to track the movement of particles in the body.