旋转位似“似”成双 定点定形“轨”一致

轨迹法是解决最值问题的重要方法.图形在绕定点作旋转加位似变换时,对应点的轨迹形状呈现一致性.这种旋转位似确定轨迹的方法,通过原理介绍和结论证明,揭示旋转位似变换中的性质和规律,并以“转移位置”“内嵌面积”“最值线段”三个方面的应用,让学生在问题分析中学会用运动变换的视角看问题,感悟到“定点加定形,轨迹形一致”的图形认识.

Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems

Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.