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Generalized Coordinate and

Generalized Force

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Contoh :

Sebuah partikel yang bergerak bebas didalam ruang.Sistem ini memerlukan 3 koordinat untuk mendeskribsikan ge-

raknya (x, y, z). Maka derajat kebebasan sistem itu adalah 3

Sebuah sistem yang mengandung N partikel yang bergerak bebas

didalam ruang.

Sistem ini memerlukan 3N koordinat untuk mendeskribsikan

geraknya, karena masing-masing partikel membutuhkan 3

koordinat sehingga totalnya adalah 3N. Maka derajat kebeba-

san sistem itu adalah 3N

Generalized Coordinate (n)

A set of coordinates or parameters, which uniquely describes the

geometric position and/or orientation of body, or system of bodies(2002. Volaeris Engineering, LLC)

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Constraint (m)the limitation of the motion(Spiegel, MR. 1983. Theoritical Mechanics. Schaums Outline Series)

Contoh :

Gerak sebuah partikel yang yang terbatas pada suatu curva

Gerak benda pejal akan sedemikian sehingga jarak antara 2

partikel penyusun benda tsb selalu sama

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Degrees of freedom of a body (DOF)

The number of independent parameters that define the displacement of

the body(Spiegel, MR. 1983. Theoritical Mechanics. Schaums Outline Series)

The minimum number of independent generalized coordinates necessary

to completely describe the geometry

(2002. Volaeris Engineering, LLC)

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Generalized Coordinate (n), Degrees of

freedom (DOF) & Constraint (m)

=

Critical point : the number of DOF is a characteristic of the system and does NOT

depend on the particular set of coordinates used to describe the configuration

(Lecture #7 .Aerospace Dynamics. Massachusetts Institute of Technology How, Deyst 2003 (Based on notes by Blair 2002))

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Examples 1 : Freely motion of a particle in space

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Examples 2 : Conical Pendulum

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Examples 3 : Double Pendulum

Generalized coordinates (x1, y1) dan (x2, y2)

n = 4

Constraint : constant length of rope (L1 and L2)

m = 2

So we can correlate betweenx1, y1 andx2, y2

= +

= +

Degrees of freedom

= = 2

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Examples 4 : freely motion of a bar

Generalized coordinates, n = 4

Constraint : constant length of bar L, m = 1

So we can correlate betweenx1, y1 andx2, y2

Degrees of freedom

= = 3

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Examples 5 : freely motion of a bar which pinned at pont A

Generalized coordinates, n = 4

Constraint :

constant length of bar L,

Degrees of freedom

= = 1

Olnly depend on

Pinned point A

xA, yA tmust be 0,0

m = 3

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Pergeseran virtual

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Gaya Tergeneralisasi

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Contoh 1

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Contoh 2

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