In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for t...In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.展开更多
Gravity-aided inertial navigation is a hot issue in the applications of underwater autonomous vehicle(UAV). Since the matching process is conducted with a gravity anomaly database tabulated in the form of a digital mo...Gravity-aided inertial navigation is a hot issue in the applications of underwater autonomous vehicle(UAV). Since the matching process is conducted with a gravity anomaly database tabulated in the form of a digital model and the resolution is 2’ × 2’,a filter model based on vehicle position is derived and the particularity of inertial navigation system(INS) output is employed to estimate a parameter in the system model. Meanwhile, the matching algorithm based on point mass filter(PMF) is applied and several optimal selection strategies are discussed. It is obtained that the point mass filter algorithm based on the deterministic resampling method has better practicability. The reliability and the accuracy of the algorithm are verified via simulation tests.展开更多
In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) ...In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.展开更多
<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines ...<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.展开更多
为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结...为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结构振动特性的影响;最后对TMDI鲁棒性进行研究。结果表明:惯容系统连接位置对阻尼器吸振能力影响显著,与传统TMD和非接地TMDI相比,接地TMDI使主结构动力放大系数分别减小约8.4%、16.5%;接地TMDI调频宽度相比传统TMD提高约6%;在阻尼摄动范围内,接地TMDI减振系统动力放大系数增幅约1.5倍;接地TMDI具有更良好的鲁棒性,可为设计新型TMDI模型提供理论参考。展开更多
文摘In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.
基金supported by the National Natural Science Foundation of China(61673060)the National Key R&D Plan(2016YFB0501700)
文摘Gravity-aided inertial navigation is a hot issue in the applications of underwater autonomous vehicle(UAV). Since the matching process is conducted with a gravity anomaly database tabulated in the form of a digital model and the resolution is 2’ × 2’,a filter model based on vehicle position is derived and the particularity of inertial navigation system(INS) output is employed to estimate a parameter in the system model. Meanwhile, the matching algorithm based on point mass filter(PMF) is applied and several optimal selection strategies are discussed. It is obtained that the point mass filter algorithm based on the deterministic resampling method has better practicability. The reliability and the accuracy of the algorithm are verified via simulation tests.
基金mostly financed by the FP7 Project ASTARTE "Assessment,Strategy and Risk Reduction for 740 Tsunamis in Europe"(FP7-ENV2013 6.4-3,Grant603839)the Italian National Project RITMARE that,among others,treat landslide models with tsunamigenic potential
文摘In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.
文摘<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.
文摘为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结构振动特性的影响;最后对TMDI鲁棒性进行研究。结果表明:惯容系统连接位置对阻尼器吸振能力影响显著,与传统TMD和非接地TMDI相比,接地TMDI使主结构动力放大系数分别减小约8.4%、16.5%;接地TMDI调频宽度相比传统TMD提高约6%;在阻尼摄动范围内,接地TMDI减振系统动力放大系数增幅约1.5倍;接地TMDI具有更良好的鲁棒性,可为设计新型TMDI模型提供理论参考。
