Classical Mechanics
Lecture 3
, 1.3: Constraints
• Many systems have CONSTRAINTS which limit their motion.
When the motion of a dynamic system is not permitted to
extend freely in three dimensions, the system is said to be
subject to constraints.
– Example: Rigid Body. Constraints keep rij = constant.
– Example: Particle motion on surface of sphere.
, Degrees of freedom
The minimum number of independent variables or coordinates required
for specifying completely the configuration or state of the system. of a
dynamical system consisting of one or more particle is called Degree of
freedom.
For the N number of particles moving freely in d dimensional space
degrees of freedom is represented by the following equation.
Where N is the number of particles and d denote the dimensions of
f
the
particle. f=Nd
If there are constraints then
f=Nd−k
where k is the number of constraints.
Lecture 3
, 1.3: Constraints
• Many systems have CONSTRAINTS which limit their motion.
When the motion of a dynamic system is not permitted to
extend freely in three dimensions, the system is said to be
subject to constraints.
– Example: Rigid Body. Constraints keep rij = constant.
– Example: Particle motion on surface of sphere.
, Degrees of freedom
The minimum number of independent variables or coordinates required
for specifying completely the configuration or state of the system. of a
dynamical system consisting of one or more particle is called Degree of
freedom.
For the N number of particles moving freely in d dimensional space
degrees of freedom is represented by the following equation.
Where N is the number of particles and d denote the dimensions of
f
the
particle. f=Nd
If there are constraints then
f=Nd−k
where k is the number of constraints.
