摘要
By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev’s model,and thus Chetaev’s model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
基金
Supported by the National Natural Science Foundation of China (Grant No. 10272034)
the Research Fund for the Doctoral Program of Higher Education of China
the Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020)
关键词
generalized
variational
principle
nonholonomic
systems
Chetaev’s
model
Vakonomic
model
the
Lagrangian
clas-sical
relationship
the
Lagrangian
theoretical
framework
generalized
variational
principle,
nonholonomic
systems,
Chetaev's
model,
Vakonomic
model,
the
Lagrangian
classical
relationship,
the
Lagrangian
theoretical
framework
By
the
generalized
variational
principle
of
two
kinds
of
variables
in
general
mechanics,
it
was
demonstrated
that
two
Lagrangian
classical
relationships
can
be
applied
to
both
holonomic
systems
and
nonholonomic
systems.
And
the
restriction
that
two
Lagrangian
classical
relationships
cannot
be
applied
to
nonholonomic
systems
for
a
long
time
was
overcome.
Then,
one
important
formula
of
similar
Lagrangian
classical
relationship
called
the
popularized
Lagrangian
classical
relationship
was
derived.
From
Vakonomic
model,
by
two
Lagrangian
classical
relationships
and
the
popularized
Lagrangian
classical
relationship,
the
result
is
the
same
with
Chetaev's
model,
and
thus
Chetaev's
model
and
Vakonomic
model
were
unified.
Simultaneously,
the
Lagrangian
theoretical
framework
of
dynamics
of
nonholonomic
system
was
established.
By
some
representative
examples,
it
was
validated
that
the
Lagrangian
theoretical
framework
of
dynamics
of
nonholonomic
systems
is
right.
……
