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  2. Kinematics - Wikipedia

    en.wikipedia.org/wiki/Kinematics

    In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and, working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. [8] In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.

  3. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    Any of the position vectors can be denoted r k where k = 1, 2, …, N labels the particles. A holonomic constraint is a constraint equation of the form for particle k [4] [a] (,) = which connects all the 3 spatial coordinates of that particle together, so they are not independent.

  4. 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.

  5. List of equations in classical mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in...

    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]

  6. Analytical mechanics - Wikipedia

    en.wikipedia.org/wiki/Analytical_mechanics

    The number of curvilinear coordinates equals the dimension of the position space in question (usually 3 for 3d space), while the number of generalized coordinates is not necessarily equal to this dimension; constraints can reduce the number of degrees of freedom (hence the number of generalized coordinates required to define the configuration ...

  7. Position and momentum spaces - Wikipedia

    en.wikipedia.org/wiki/Position_and_momentum_spaces

    Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.)

  8. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. [16] In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as ...

  9. Euler's laws of motion - Wikipedia

    en.wikipedia.org/wiki/Euler's_laws_of_motion

    Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]