Game Development Reference

In-Depth Information

a v
is the acceleration of the particle in the rotating reference

frame. The total linear acceleration

()

()

where

t

=

t

r

r

()

a

t

of the particle is thus given by

()

()

()

()

()

()

()

a

t

= = ×+ ×+

=

v ω r ω r a

ω r ω r ω v

t

t

t

t

t

t

f

()

()

()

()

()

()

()

t

×

t

+

t

×

t

+

t

×

t

+

a

t

.

(14.11)

r

r

()

()

Since

r
is equal to the linear velocity

t

v

t

of the particle, we can write

]

a ω r ωωr

()

t

=

()

t

×

()

t

+

()

t

×

()

t

×

()

t

+

2

ω v

()

t

×

()

t

+

a

()

t

. (14.12)

[

r

r

()

The force

F

t

experienced by the particle is therefore

()

()

()

()

()

()

()

]

t

=

mt

a

=

mt

ω r

×

t

+

mt

ωωr

×

t

×

t

F

[

()

()

()

+

2

mt

ω v

×

t

+

m t

a

.

(14.13)

r

r

()

In the reference frame of the rotating system, the force

t

on the object ap-

F

r

pears to be the following.

]

()

()

()

()

()

()

()

()

F

t

=

mt

a

=

F

t

−

mt

ω r

×

t

−

mt

ωωr

×

[

t

×

t

r

r

()

()

−

2

mt

ω v

×

t

(14.14)

r

As expected, the centrifugal force shows up again, but there is also a new term

called the
Coriolis force
that acts on the particle in a direction perpendicular to its

velocity in the rotating reference frame (see Figure 14.4). The Coriolis force,

given by

()

()

=−

2

mt

ω v

×

t

,

(14.15)

F

Coriolis

r

()

ω

t

() ()

2

mt

ωv

t

r

()

v

r
t

()

r

t

α

O

Figure 14.4.
The Coriolis force.

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