“Rheonomous”的意思、由来-开放百科全书

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Rheonomous

释义

Example: simple 2D pendulum
See also
References

A mechanical system is rheonomous if its equations of constraints contain the time as an explicit variable.^[1]^[2] Such constraints are called rheonomic constraints. The opposite of rheonomous is scleronomous.^[1]^[2]

Example: simple 2D pendulum

As shown at right, a simple pendulum is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length. Therefore, this system is scleronomous; it obeys the scleronomic constraint

,

where is the position of the weight and the length of the string.

The situation changes if the pivot point is moving, e.g. undergoing a simple harmonic motion

,

where is the amplitude, the angular frequency, and time.

Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore, this system is rheonomous; it obeys the rheonomic constraint

.

References

1. ^¹{{cite book |last=Goldstein |first=Herbert |authorlink=Herbert Goldstein |title=Classical Mechanics |year=1980 |location=United States of America |publisher=Addison Wesley |edition=2nd |isbn=0-201-02918-9 |page=12 |quote=Constraints are further classified according as the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous).}}
2. ^¹{{cite book |last=Spiegel |first=Murray R. |title=Theory and Problems of THEORETICAL MECHANICS with an Introduction to Lagrange's Equations and Hamiltonian Theory |year=1994 |series=Schaum's Outline Series |publisher=McGraw Hill |isbn=0-07-060232-8 |page=283 |quote=In many mechanical systems of importance the time t does not enter explicitly in the equations (2) or (3). Such systems are sometimes called scleronomic. In others, as for example those involving moving constraints, the time t does enter explicitly. Such systems are called rheonomic.}}

3 : Mechanics|Classical mechanics|Lagrangian mechanics

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Example: simple 2D pendulum

See also

References