In the present paper, using a generalization of the Miyamoto and Nagai potential we adjusted the observed rotation curves of three specific spiral galaxies to the analytical circular velocities. The observational data have been taken from a 21 cm-line synthesis imaging survey using the Westerbork Synthesis Radio Telescope, for three particular galaxies in the Ursa Major cluster: NGC 3726, NGC 3877 and NGC 4010. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method, finding that for larger values of the angular momentum of the test particle or lower values its total energy the dynamics is mainly regular, while on the opposite cases, the dynamics is mainly chaotic. Our toy model opens the possibility to find chaotic bounded orbits for stars in those particular galaxies.Dinámica orbital en modelos realistas de galáxias: NGC 3726, NGC 3877 y NGC 4010 ResumenEn el presente trabajo, utilizando una generalización del potencial de Miyamoto-Nagai, se ajustan las curvas de rotación observadas de tres galaxias espirales a las velocidades circulares analíticas. Los datos observacionales se tomaron de un conjunto de imágenes de línea de 21 centímetros (o línea HI) obtenidos con el Westerbork Synthesis Radio Telescope (WSRT), para tres galaxias particulares en el grupo de la Ursa Major: NGC 3726, NGC 3877 y NGC 4010. Seguidamente, se analiza la dinámica del sistema en términos del método de secciones de Poincaré, encontrando que para valores grandes del momento angular de la partícula de prueba o valores bajos su energía total, la dinámica es principalmente regular, mientras que en los casos opuestos, la dinámica es principalmente caótica. Nuestro modelo abre la posibilidad de encontrarórbitas caóticas acotadas para estrellas presentes en esas galaxias particulares.Palabras clave: Dinámica estelar, Galaxias: cinemática y dinámica, Dinámica no lineal y caos.
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