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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.
In physics, a projectile launched with specific initial conditions will have a range. It may be more predictable assuming a flat Earth with a uniform gravity field , and no air resistance . The horizontal ranges of a projectile are equal for two complementary angles of projection with the same velocity.
In projectile motion, the horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. This is the principle of compound motion established by Galileo in 1638, [1] and used by him to prove the parabolic form of projectile motion. [2]
The motion is simple harmonic motion where θ 0 is the amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical). The corresponding approximate period of the motion is then
The last equation is more accurate where significant changes in fractional distance from the centre of the planet during the fall cause significant changes in g. This equation occurs in many applications of basic physics. The following equations start from the general equations of linear motion:
Numerically, a vector can be represented as a list; for example, a body's velocity vector might be = ( /, /), indicating that it is moving at 3 metres per second along the horizontal axis and 4 metres per second along the vertical axis. The same motion described in a different coordinate system will be represented by different numbers, and ...
Hamilton's equations give the time evolution of coordinates and conjugate momenta in four first-order differential equations, ˙ = ˙ = ˙ = ˙ = Momentum , which corresponds to the vertical component of angular momentum = ˙ , is a constant of motion. That is a consequence of the rotational symmetry of the ...
In physics, circular motion is movement of an object along the circumference of a ... The equations of motion describe the movement of the ... vertical loop: 100 mm/s ...