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The work W done by a constant force of magnitude F on a point that moves a displacement s in a straight line in the direction of the force is the product = For example, if a force of 10 newtons ( F = 10 N ) acts along a point that travels 2 metres ( s = 2 m ), then W = Fs = (10 N) (2 m) = 20 J .
In classical mechanics, the Udwadia–Kalaba formulation is a method for deriving the equations of motion of a constrained mechanical system. [1] [2] The method was first described by Anatolii Fedorovich Vereshchagin [3] [4] for the particular case of robotic arms, and later generalized to all mechanical systems by Firdaus E. Udwadia and Robert E. Kalaba in 1992. [5]
In the application of the principle of virtual work it is often convenient to obtain virtual displacements from the velocities of the system. For the n particle system, let the velocity of each particle P i be V i, then the virtual displacement δr i can also be written in the form [2] = = ˙, =, …,.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The inertial force must act through the center of mass and the inertial torque can act anywhere. The system can then be analyzed exactly as a static system subjected to this "inertial force and moment" and the external forces. The advantage is that in the equivalent static system one can take moments about any point (not just the center of mass).
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.
The formula above for the principle of virtual work with applied torques yields the generalized force = = / = The mechanical advantage of the gear train is the ratio of the output torque T B to the input torque T A , and the above equation yields M A = T B T A = R . {\displaystyle MA={\frac {T_{B}}{T_{A}}}=R.}
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 ...