![]() ![]() To consider rigid body dynamics in three-dimensional space, Newton's second law must be extended to define the relationship between the movement of a rigid body and the system of forces and torques that act on it. When used to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions. ![]() With respect to rotation vectors, they can be more easily converted to and from matrices. They are equivalent to rotation matrices and rotation vectors. Main article: Quaternions and spatial rotationĪnother way to describe rotations is using rotation quaternions, also called versors. Determine the resultant force and torque at a reference point R, to obtain In this case, Newton's laws (kinetics) for a rigid system of N particles, P i, i=1., N, simplify because there is no movement in the k direction. If a system of particles moves parallel to a fixed plane, the system is said to be constrained to planar movement. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law ( kinetics) or their derivative form, Lagrangian mechanics. This excludes bodies that display fluid, highly elastic, and plastic behavior. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. The assumption that the bodies are rigid (i.e. \begin$ have not changed.In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The relationship between acceleration and the force caused by that acceleration is given by Newton's second law: Once the car stops accelerating and maintains a constant velocity, that force goes away. As the car accelerates forward, you would feel a force pushing you back into your seat. Another example of this is the experience of a passenger in an accelerating car. ![]() This is because acceleration is, in turn, always associated with some unbalanced (net) force on a body. Inside the train, you can tell that your velocity has changed because you can feel the acceleration manifested as an unbalanced force on your body. A change in velocity is always caused by an acceleration. You may start moving vertically a bit upwards after hitting the bump and then downwards again due to gravity. If you hit a bump, your velocity changes. You, and the coffee, are in static equilibrium. You can comfortably enjoy a nice cup of hot coffee without spilling it all over yourself (again, unless you hit a bump). If you are sitting in a train, moving at constant velocity, it feels just like you are sitting still (except for any bumps in the road that momentarily change your velocity). Why is this the case? According to relativity (Einstein), it is not possible to tell if an object is moving or not from the point of view of an observer on the object if that object is moving at a constant velocity. ![]() This means that it is moving at a constant velocity. Technically, a body (or structure) is in static equilibrium if it is not accelerating. >When you're done reading this section, check your understanding with the interactive quiz at the bottom of the page. ![]()
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