造父变星型振子
造父变星型振子,1955年天文学家W.S。Krogdahl在天体物理学学报上发表《天体的搏动是一种极限环现象》[1]。
Krogdahl用下列非线性常微分方程组模拟造父变星的半径随时间的变化[2]:
造父变星的半径变化用下式表达:
此微分方程组无解析解,但可以用龙格-库塔法定性求得数值图解。
设参数params := a = .1*(1/3), b = .5,c=10;
初始条件:init:= x(0) = 1.1, y(0) = 0
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Cepheid_varible_star_radius_plot.png/500px-Cepheid_varible_star_radius_plot.png)
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Cepheid_varible_star_limit_cycle.png/300px-Cepheid_varible_star_limit_cycle.png)
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Cepheid_varible_star_pulsator_phase_diagram.png/300px-Cepheid_varible_star_pulsator_phase_diagram.png)
参考文献
- ^ W.S.Krogdahl Stellar Pulsation as a limit cycle phenomena. Astrophysical Journal, 122:43,1955
- ^ Richard H.Enns & George C. McGuire Nonlinear Physics with Maple for Scientists and Engineers, p189