Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds: A Geometric Approach To Modeling And Analysis (interaction Of Mechanics And Mathematics)
by N. Harris McClamroch /
2017 / English / PDF
6.4 MB Download
This book provides an accessible introduction to the variational
formulation of Lagrangian and Hamiltonian mechanics, with a novel
emphasis on global descriptions of the dynamics, which is a
significant conceptual departure from more traditional approaches
based on the use of local coordinates on the configuration
manifold. In particular, we introduce a general methodology for
obtaining globally valid equations of motion on configuration
manifolds that are Lie groups, homogeneous spaces, and embedded
manifolds, thereby avoiding the difficulties associated with
coordinate singularities.
This book provides an accessible introduction to the variational
formulation of Lagrangian and Hamiltonian mechanics, with a novel
emphasis on global descriptions of the dynamics, which is a
significant conceptual departure from more traditional approaches
based on the use of local coordinates on the configuration
manifold. In particular, we introduce a general methodology for
obtaining globally valid equations of motion on configuration
manifolds that are Lie groups, homogeneous spaces, and embedded
manifolds, thereby avoiding the difficulties associated with
coordinate singularities.
The material is presented in an approachable fashion by
considering concrete configuration manifolds of increasing
complexity, which then motivates and naturally leads to the more
general formulation that follows. Understanding of the material
is enhanced by numerous in-depth examples throughout the book,
culminating in non-trivial applications involving multi-body
systems.
The material is presented in an approachable fashion by
considering concrete configuration manifolds of increasing
complexity, which then motivates and naturally leads to the more
general formulation that follows. Understanding of the material
is enhanced by numerous in-depth examples throughout the book,
culminating in non-trivial applications involving multi-body
systems.
This book is written for a general audience of mathematicians,
engineers, and physicists with a basic knowledge of mechanics.
Some basic background in differential geometry is helpful, but
not essential, as the relevant concepts are introduced in the
book, thereby making the material accessible to a broad audience,
and suitable for either self-study or as the basis for a graduate
course in applied mathematics, engineering, or physics.
This book is written for a general audience of mathematicians,
engineers, and physicists with a basic knowledge of mechanics.
Some basic background in differential geometry is helpful, but
not essential, as the relevant concepts are introduced in the
book, thereby making the material accessible to a broad audience,
and suitable for either self-study or as the basis for a graduate
course in applied mathematics, engineering, or physics.
