准确,负担得起和无监督:由一般化内部坐标驱动的分析F12梯度

The central force system operates by exerting a force on an object directed towards a fixed point, typically the origin, with the force magnitude determined by the object's distance from this fixed point. In the context of an object with mass 'm,' polar coordinates are employed to express the equation of motion. Notably, the azimuthal component of force is nonexistent in this system. A comprehensive rewrite and integration of this equation reveal that the product of the squared...

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the...

In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...