Short course on differential-geometric methods in computational multibody system dynamics


Udine, Italy, September 16 - 20, 2013
CISM-Centre International des Sciences Me?caniques (International Centre
for Mechanical Sciences)

Advanced School coordinated by Zdravko Terze (University of Zagreb,
Croatia) and Andreas Mueller (Technical University of Chemnitz, Germany)

Introduction: Multibody system (MBS) dynamics, a branch of computational
mechanics dealing with modeling principles and computational methods for
dynamic analysis, simulation and control of mechanical systems, requires
efficient and reliable formulations and computational methods. Within
research of novel computational concepts, geometric aspects of kinematical
and dynamical modeling of MBS are increasingly recognized to play a
significant role. By operating on manifolds, and Lie-groups in particular,
instead of linear vector spaces, geometric algorithms respect the geometric
structure underlying many technical systems and hence offer attractive
features such as numerical robustness and efficiency as well as avoidance
of the kinematical singularities. Also, it is well-known that
differential-geometric methods are the key concepts in contemporary
mechanism design, and control theory. As such, geometric methods can
provide the unifying mathematical framework that allows for successful
studying of multidisciplinary interactions within complex environments.

Objective and Audience: The aim of the School is to deliver a panoramic
overview of the mathematical concepts underlying modern geometric
approaches to modeling, time integration, and control of MBS, followed by
an in-depth introduction to the relevant computational algorithms and
numerical methods. By merging geometric methods in MBS dynamics, non-linear
control and mechanism theory, the School provides a unique educational
platform that will deliver novel modeling concepts as well as theoretical
and computational insights into dynamics and control of mechanical systems.
The lectures take an application-driven approach, and numerous case-studies
from many fields of engineering are presented and documented. The School is
primarily aimed for the audience of doctoral students and young researchers
(post-docs) in engineering, mathematics and applied physics, but will be
valuable also for senior researchers and practicing engineers who are
interested in the field.

Lectures Outline: The lectures provide a hands-on introduction to
differential-geometric foundations and the audience will make acquaintance
with these topics in a natural and application-driven way. A central topic
of the school is efficient formulations using Lie-group concepts and screw
theory, giving rise to numerically efficient and stable algorithms for MBS
comprising rigid and flexible members. Special focus is given to energy and
structure preserving numerical integration methods on manifolds for
discrete and continuous systems. Natural coupling between mathematical
modeling, numerical integration and control issues are covered by the
lectures on variational integrators and optimal control with structure
preserving integrators. Specifically, lectures will include:
• introduction to mathematical concepts and differential-geometric modeling
(manifolds, Lie-groups, Lie-algebras, exponential maps, screw theory etc.);
• modeling of complex MBS using compact Lie- group formalisms;
• time integration on Lie-groups;
• geometrically exact formulations for beams and shells;
• energy-consistent time integration procedures for MBS with flexible
• numerical treatment of holonomic and non-holonomic constraints,
constraint stabilization;
• variational integrators, discrete mechanics and optimal control using
structure-preserving integration schemes applied to high degree-of-freedom
• Lie- group/screw theoretic framework for design of MBS and articulated
• multi-physics coupling procedures: aero-servo- elastic multidisciplinary
models and applications.
A treatment of many numerical case-studies in the domain of robotics, wind
energy systems, rotorcraft dynamics, aeronautical and mechatronical systems
will highlight compact formulations, relevance and computational advantages
of the geometric approach in the modern computational mechanics. The
unifying lecturing approach that combines computational procedures, control
algorithms and design aspects, and provides new insights into the coupled
modeling procedures, makes this School unique.

Zdravko Terze - University of Zagreb, Croatia
Andreas Mueller - Technical University of Chemnitz, Germany
Xilun Ding - Beijing University of Aero. & Astro, China
Olivier Bruels - University of Lie?ge, Belgium
Carlo Bottasso - Politecnico di Milano, Italy
Todd Murphey - Northwestern University, United States

All lectures will be given in English. Lecture notes can be downloaded from
CISM web site, instructions will be sent to accepted participants.

Applicants must apply at least one month before the beginning of the
course. Application forms should be sent on-line through our web site: or by post.
A message of confirmation will be sent to accepted partici- pants. If you
need assistance for registration please contact our secretariat.
The 700,00 Euro registration fee includes a complimentary bag, four fixed
menu buffet lunches (Friday not included), hot beverages,
on-line/downloadable lecture notes and wi-fi internet access.
A limited number of participants from universities and research centres who
are not supported by their own institutions can be offered board and/or
lodging in a reasonably priced hotel. Requests should be sent to CISM
Secretariat by July 16, 2013 along with the applicant's curriculum and a
letter of recommendation by the head of the department or a supervisor
confirming that the institute cannot provide funding. Preference will be
given to applicants from countries that sponsor CISM.
Information about travel and accommodation is available on our web site, or
can be mailed upon request.
Please note that the centre will be closed for summer vacation the first
three weeks in August.

CISM Short Courses are currently part of Doctoral programmes in a number of
European Universities and Higher Education Institutes. Upon agreement
between CISM representatives, course coordinators and the director of the
specific doctoral school, short courses can award credits for doctoral
programmes. A list of European Universities acknowledging CISM courses in
the frame of doctoral programmes includes TU Munich, TU Wien, ETH Zurich,
JKU Linz, and University of Udine.  For more information, please go to
For more information about the short course please feel free to contact
Prof. Todd Murphey at

Todd Murphey
Associate Professor
Mechanical Engineering
Physical Therapy and Human Movement Sciences
Northwestern University