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An elastically deformable mass deforms under an applied force (or acceleration); the deformation is a function of its stiffness and the magnitude of the force. If the change in force is slow, the jerk is small, and the propagation of deformation is considered instantaneous as compared to the change in acceleration.
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by ...
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.
Linear motion, also called rectilinear motion, [1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non ...
In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it (Newton's second law): = =, where F is the net force acting on the body, m is the mass of the body, and a is the center-of-mass acceleration.
Euler's second axiom or law (law of balance of angular momentum or balance of torques) states that in an inertial frame the time rate of change of angular momentum L of an arbitrary portion of a continuous body is equal to the total applied torque M acting on that portion, and it is expressed as. where is the velocity, the volume, and the ...
The total (mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = ma, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e. its ...
Trajectory. A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.