476
F. Scheaua
Fig. 2 Simplified schematic
representation of motion
components on supports
R
2
= u
2
+ (R − h)
2
(2)
h
2
− 2Rh + u
2
= 0
( 3 )
The accepted relation from the geometric conditions for vertical elevation (h) is
the following [5]:
h = R −
R 2 − u 2
(4)
The simplified schematic presentation as well as the physical modeling of the
spherical sliding system functioning based on the dry friction force (Coulomb) is
shown in Fig. 3.
Physical modeling describing the operation of the spherical rolling pendulum
support is performed and the relations describing the forces equilibrium involved in
the operation of the friction insulating system are as follows [5]:
P − N cos ϕ + F f sin ϕ = 0
F − N sin ϕ − F f cos ϕ = 0
( 5 )
By multiplying the two equations with (− sin ϕ) and (cos ϕ), respectively, are
obtained the following equations:
Fig. 3 Physical modeling of
the spherical rolling isolation
support operation
F. Scheaua
Fig. 2 Simplified schematic
representation of motion
components on supports
R
2
= u
2
+ (R − h)
2
(2)
h
2
− 2Rh + u
2
= 0
( 3 )
The accepted relation from the geometric conditions for vertical elevation (h) is
the following [5]:
h = R −
R 2 − u 2
(4)
The simplified schematic presentation as well as the physical modeling of the
spherical sliding system functioning based on the dry friction force (Coulomb) is
shown in Fig. 3.
Physical modeling describing the operation of the spherical rolling pendulum
support is performed and the relations describing the forces equilibrium involved in
the operation of the friction insulating system are as follows [5]:
P − N cos ϕ + F f sin ϕ = 0
F − N sin ϕ − F f cos ϕ = 0
( 5 )
By multiplying the two equations with (− sin ϕ) and (cos ϕ), respectively, are
obtained the following equations:
Fig. 3 Physical modeling of
the spherical rolling isolation
support operation