ON THE BIFURCATION AND STABILITY OF THE STEADY-STATE MOTIONS OF COMPLEX MECHANICAL SYSTEMSстатья
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Дата последнего поиска статьи во внешних источниках: 22 июля 2017 г.
Аннотация:Many
objects
of
modern
technology
(rockets,
spaceships,
airplanes,
gyroscopic
devices,
centrifuges,
etc.
)
can
be
modelled
in
a
number
of
cases
by
mechanical
systems
comprised
of
absolutely
rigid
bodies
and
material
points
and
of
deform-
able
(liquid
and
elastic)
bodies
connected
with
them.
Mechanical
systems
con-
taining
among
its
parts
both
subsystems
with
a
finite
number
of
degrees
of
free-
dom
as
well
as
units
with
distributed
parameters,
i.
e.
continuous
media,
are
called
complex
systems
for
brevity.
We
consider
the
steady-state
motions
of
complex
systems.
Stationary
values
of
the
potential
energy
V
or
of
the
altered
potential
energy
FV
of
the
system
correspond
to
the
steady-state
motions.
The
stability
problem
for
the
steady-state
motions
leads
to
the
investigation
of
the
nature
of
the
extremum
of
the
potential
energy
V
or
W.
The
minimum
of
the
potential
energy
corresponds
to
a
stable
motion.
In
a
number
of
important
cases
the
stability
(instability)
conditions
can
be
obtained
as
conditions
for
the
positive
definiteness
(for
sign-alteration
together
with
certain
additional
conditions)
of
the
second
variation
baV
or
FW
of
the
potential
energy.
These
general
results
are
applied
to
solving
a
number
of
concrete
problems
on
the
stability
of
the
steady-state
motions
of
complex
systems.
Stability
conditions
for
the
motion
of
a
rigid
body
with
liquid
and
elastic
parts
in
various
force
fields
are
discussed.