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Shear Diagram01:27

Shear Diagram

1.5K
In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
First, a free-body diagram of the beam is drawn, representing all the external forces and internal reactions acting on the beam. One can calculate the reaction forces at each support by employing the equilibrium equations of force and moment. The vertical component...
1.5K
Non-conservative Forces01:17

Non-conservative Forces

9.3K
Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike conservative forces, non-conservative forces do not have potential energy associated with them. This is because the energy is lost to the system and cannot be turned into useful work later.
Also unlike their conservative counterparts, they are path-dependent; where the object starts and stops does matter. For example, a grinding wheel applies a...
9.3K
Conservative Forces01:14

Conservative Forces

13.7K
According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of...
13.7K
Conservative Forces01:03

Conservative Forces

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Conservative forces are an essential concept in the field of mechanical engineering. Understanding the properties and characteristics of these forces is crucial to the design and analysis of mechanical systems.
Conservative forces are forces that are dependent only on the initial and final positions of an object and that are independent of the path that the object takes between these positions. These forces conserve energy, which means that the work done by the force is independent of the path...
883
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

3.0K
When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
3.0K
Shearing Strain01:20

Shearing Strain

1.2K
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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Generation of Shear Adhesion Map Using SynVivo Synthetic Microvascular Networks
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保存則的な池田写像におけるシアレスバリア

Rodrigo Simile Baroni1, Ricardo Egydio de Carvalho2, José Danilo Szezech Junior3

  • 1Universidade de São Paulo (USP), Instituto de Física, São Paulo, SP 05508-900, Brazil.

Physical review. E
|December 23, 2025
PubMed
まとめ

2次元面積保存系である池田写像は、非積分極限においてシアレスバリアを示す。これらのバリアは制御パラメータに基づいて出現・持続し、系のダイナミクスに影響を与える。

キーワード:
池田写像保存極限面積保存写像シアレスバリア非線形力学系パラメータ依存性

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科学分野:

  • 　　力学系
  • 　　非線形力学
  • 　　数理物理学

背景:

  • 　　池田写像は2次元面積保存写像である。
  • 　　制御パラメータθおよびφによって支配される。
  • 　　写像は回転と平行移動の合成として見ることができる。

研究 の 目的:

  • 　　保存極限における池田写像のダイナミクスを調査する。
  • 　　シアレスバリアの形成と挙動を解析する。
  • 　　バリアダイナミクスに対する制御パラメータの影響を理解する。

主な方法:

  • 　　写像を回転と平行移動の合成として解釈する。
  • 　　積分可能な場合（φ=0）を均一な回転として解析する。
  • 　　座標依存の回転を伴う非積分な場合（φ≠0）を研究する。
  • 　　バリア形成を示す極値について回転数プロファイルを調べる。
  • 　　パラメータ変化によるバリアの出現、持続、崩壊を解析する。

主要な成果:

  • 　　φ=0の積分可能な場合、池田写像は一様な回転である。
  • 　　φ≠0の場合、写像は座標依存の回転を伴う非積分系となる。
  • 　　回転数プロファイルにおける極値は、シアレスバリアの形成を示唆する。
  • 　　これらのバリアは、制御パラメータθおよびφに応じて出現、持続、および崩壊する。

結論:

  • 　　池田写像の保存極限ダイナミクスは、非積分領域におけるシアレスバリアによって特徴付けられる。
  • 　　これらのバリアの存在と安定性は、制御パラメータに敏感である。
  • 　　本研究は、面積保存写像の複雑なダイナミクスに関する洞察を提供する。