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Updated: Jun 13, 2025

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运动方程规范化轨道优化的二次扰动理论与密度合适的近似方法.

Aslı Ünal1, Uğur Bozkaya1

  • 1Department of Chemistry, Hacettepe University, Ankara 06800, Turkey.

The Journal of chemical physics
|September 16, 2024
PubMed
概括

新的计算方法,K-DF-EOM-OMP2和K-DF-EOM-MP2,为化学系统提供高度准确的激发能量. 这些方法以较低的成本接近合集群质量,为激发状态研究提供了宝贵的工具.

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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Equation of Motion for a Rigid Body01:12

Equation of Motion for a Rigid Body

The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
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Equation of Rotational Dynamics01:08

Equation of Rotational Dynamics

Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
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In the context of a rigid body's movement within a general plane, it is important to understand that this motion is typically triggered by external forces or couple moments exerted onto it. This principle can be explained through Newton's second law, which stipulates the translational motion of the body's center of mass along each axis.
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Central-Force Motion

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...
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Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
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