1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability
Rent:
Rent this article for
USD
10.1063/1.1920287
/content/aip/journal/jmp/46/6/10.1063/1.1920287
http://aip.metastore.ingenta.com/content/aip/journal/jmp/46/6/10.1063/1.1920287
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Plot of as a function of , for and three different values of the energy: , and .

Image of FIG. 2.
FIG. 2.

Phase space trajectories, for , in the neighborhood of the origin.

Image of FIG. 3.
FIG. 3.

“Figure eight” in the plane corresponding to and energies (thick curve) and (dash curve).

Image of FIG. 4.
FIG. 4.

Plot of as a function of , for () and three different values of the energy: (small thick curve), (middle curve), and (curve with great oscillations). The curve is very similar to a pure sine or cosine curve but, for higher values of , the plot shows clearly the effects of the nonlinearity.

Image of FIG. 5.
FIG. 5.

Phase trajectories corresponding to four different values of the energy (, 0.4, 0.6, and 0.8). The trajectories are closed curves representing periodic motions that for small values of can be considered as rather similar to ellipses; for other values of the curves modify their shape and they lengthen toward the upper side of the phase plane. The motion is asymmetric in the sense that the particle moves from right to left in a slowly way but returns, from left to right, with a much higher velocity that takes its maximum value at the center point .

Image of FIG. 6.
FIG. 6.

Closed trajectories (ellipses in the linear case) in the plane corresponding to and four different values of the energy (, 0.4, 0.6 and 0.8).

Image of FIG. 7.
FIG. 7.

Nonlinear Lissajous figures in the plane corresponding to “figure eight” trajectories associated to and energies (small eight-looking curve) and (big butterfly-looking curve).

Loading

Article metrics loading...

/content/aip/journal/jmp/46/6/10.1063/1.1920287
2005-05-20
2014-04-25
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability
http://aip.metastore.ingenta.com/content/aip/journal/jmp/46/6/10.1063/1.1920287
10.1063/1.1920287
SEARCH_EXPAND_ITEM