[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*Subject*: Today's CfA Theory Seminar*From*: Kentaro Nagamine <knagamin cfa harvard edu>*Date*: Tue, 30 Sep 2003 09:06:02 -0400 (EDT)*List-archive*: <http://cosmos.phy.tufts.edu/mhonarc/bapc>*List-help*: <mailto:bapc-request@cosmos.phy.tufts.edu?subject=help>*List-id*: Boston Area Physics Calendar <bapc.cosmos.phy.tufts.edu>*List-subscribe*: <https://cosmos.phy.tufts.edu/mailman/listinfo/bapc>, <mailto:bapc-request@cosmos.phy.tufts.edu?subject=subscribe>*List-unsubscribe*: <https://cosmos.phy.tufts.edu/mailman/listinfo/bapc>, <mailto:bapc-request@cosmos.phy.tufts.edu?subject=unsubscribe>

************************************** *** CfA Theory group lunch seminar *** ************************************** Tue, Sep 30, 12:30pm Michael Efroimsky (US Naval Observatory) "Implicit Gauge Invariance in the N-body Problem of Celestial Mechanics: Practical Applications" The seminar will be held in Pratt Conference Room (G04) at CfA, 60 Garden St. Following is the abstract of the talk. ------------------------------------------------------------ We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom of choice (=freedom of gauge fixing) reveals a symmetry hiding behind Lagrange's and Delaunay's systems, which is, mathematically, analogous to the gauge invariance in electrodynamics. Historically, Lagrange removed this freedom by imposing, "by hand", a convenient constraint. This was the condition of the instantaneous ellipse (or hyperbola) being always tangential to the physical velocity. It turns out that the Lagrange constraint is also implicitly instilled into the Hamilton-Jacobi treatment of the N-body problem. Imposure of any supplementary condition different from the Lagrange constraint (but compatible with the equations of motion) is legitimate and will not alter the physical trajectory or velocity (though will much alter the mathematical form of the planetary equations). Existence of this internal freedom has consequences for the stability of numerical integrators. Another important aspect of this symmetry is that any gauge different from that of Lagrange makes the Delaunay system non-canonical. In a more general setting, when the disturbance depends not only upon positions but also upon velocities, there exists a "generalised Lagrange gauge" wherein the Delaunay system is symplectic. This special gauge renders orbital elements that are osculating in the phase space. It coincides with the regular Lagrange gauge when the perturbation is velocity-independent. We provide a practical example illustrating how the gauge formalism considerably simplifies the calculation of satellite motion about an oblate precessing planet. ------------------------------------------------------------

- Prev by Date:
**BU Condensed Matter Seminar** - Next by Date:
**CANCELLED: Joint Theory Seminar at Harvard** - Previous by thread:
**BU Condensed Matter Seminar** - Next by thread:
**Today's CfA theory seminar** - Index(es):