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AP Physics C: Mechanics and AP Physics 1 are both introductory college-level courses in mechanics, with the former recognized by more universities. [1] The AP Physics C: Mechanics exam includes a combination of conceptual questions, algebra-based questions, and calculus-based questions, while the AP Physics 1 exam includes only conceptual and algebra-based questions.
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.
Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics. [2] [3] More recently, many practical heuristic algorithms based on stochastic optimization and iterative sampling were developed, by a wide range of authors, to address the kinodynamic planning problem. These ...
[4] [5] [6] A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined.
The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters values. Remarkably, while the forward kinematics of a serial chain is a direct calculation of a single matrix equation, the forward kinematics of a parallel chain requires the simultaneous solution of multiple matrix ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
If both masses are the same, we have a trivial solution: = =. This simply corresponds to the bodies exchanging their initial velocities with each other. [ 2 ] As can be expected, the solution is invariant under adding a constant to all velocities ( Galilean relativity ), which is like using a frame of reference with constant translational velocity.
In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a screw displacement. A direct Euclidean isometry in three dimensions involves a translation and a rotation. The screw displacement representation of the isometry decomposes the translation into two components, one ...