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  2. Projectile motion - Wikipedia

    en.wikipedia.org/wiki/Projectile_motion

    This is the equation of a parabola, so the path is parabolic. The axis of the parabola is vertical. If the projectile's position (x,y) and launch angle (θ or α) are known, the initial velocity can be found solving for v 0 in the afore-mentioned parabolic equation:

  3. Parabolic trajectory - Wikipedia

    en.wikipedia.org/wiki/Parabolic_trajectory

    The green path in this image is an example of a parabolic trajectory. A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red. The height of the kinetic energy decreases ...

  4. Parabola of safety - Wikipedia

    en.wikipedia.org/wiki/Parabola_of_safety

    The paraboloid of revolution obtained by rotating the safety parabola around the vertical axis is the boundary of the safety zone, consisting of all points that cannot be hit by a projectile shot from the given point with the given speed.

  5. Paraboloidal coordinates - Wikipedia

    en.wikipedia.org/wiki/Paraboloidal_coordinates

    Similarly, the separated equations for the Laplace equation can be obtained by setting = in the above. Each of the separated equations can be cast in the form of the Baer equation . Direct solution of the equations is difficult, however, in part because the separation constants α 2 {\displaystyle \alpha _{2}} and α 3 {\displaystyle \alpha _{3 ...

  6. Fermat's spiral - Wikipedia

    en.wikipedia.org/wiki/Fermat's_spiral

    A complete Fermat's spiral (both branches) is a smooth double point free curve, in contrast with the Archimedean and hyperbolic spiral. Like a line or circle or parabola, it divides the plane into two connected regions. Definition of sector (light blue) and polar slope angle α

  7. Equations of motion - Wikipedia

    en.wikipedia.org/wiki/Equations_of_motion

    There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.

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