Linearized equations of motion are important in engineering applications, especially
with respect to stability analysis and control design. Traditionally, the full, nonlinear
equations are formed and then linearized about the desired equilibrium configuration
using methods such as Taylor series expansions.
However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical
systems. Here, this development is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems, where a hybrid
system is described with both discrete and continuous generalized coordinates. The
results presented require only velocity level kinematics to form the Lagrangian and
find equilibrium configuration(s) for the system. A set of partial derivatives of the
Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest. This study shows
that the entire nonlinear equations of motion do not have to be generated in order
to construct the linearized equations of motion. Several examples are presented to
illustrate application of these results to both continuous and hybrid system problems.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2407 |
| Date | 15 May 2009 |
| Creators | Parish, Julie Marie Jones |
| Contributors | Hurtado, John E. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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