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M. next
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In Hamilton Jacobi Equation (Projectile in two dimentions [x,y]), Isn't it correct that x is a cyclical coordinate?
Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path known as a parabola.
The equation for projectile motion is: y = y0 + v0t + (1/2)at2, where y is the final vertical position, y0 is the initial vertical position, v0 is the initial velocity, t is time, and a is acceleration due to gravity.
In horizontal motion, the object's velocity remains constant, while in vertical motion, the object's velocity changes due to the influence of gravity. However, both horizontal and vertical motion are occurring simultaneously in projectile motion.
Air resistance can slow down the horizontal velocity of a projectile, causing it to travel a shorter distance. It also affects the vertical motion, making the object experience a smaller acceleration due to gravity.
The range of a projectile can be affected by the initial velocity, angle of projection, air resistance, and the height of the launch point. It can also be affected by external factors such as wind and air density.