A mechanical system is scleronomous if the equations of constraintss do not contain the time as an explicit variable and the equation of constraints can be described by generalized coordinates. Such constraints are called scleronomic constraints. The opposite of scleronomous is rheonomous.

Application

has kinetic energy

. Use chain rule for several variables are generalized coordinates.

Rearranging the terms carefully,

are respectively homogeneous functions of degree 0, 1, and 2 in generalized velocities. If this system is scleronomous, then the position does not depend explicitly with time:

Kinetic energy is a homogeneous function of degree 2 in generalized velocities.

Example: pendulum

As shown at right, a simple pendulum is length of the string.

Take a more complicated example. Refer to the next figure at right, Assume the top end of the string is attached to a pivot point undergoing a simple harmonic motion

is time.

See also

• Lagrangian mechanics

• Holonomic system

• Nonholonomic system

• Rheonomous

• Mass matrix

References

de:Skleronom