Inequality constraints

[daniel_i_l]

In many tutorials that I've read, such as the slideshow here:
(add periods and slashes)
www gphysics com downloads The collision resolution constraints are modeled as inequalities rather than equalities. But I don't understand, why cant the euqations be written exactly using the impulse equation (the one on chris heckers sight for example) and then solve the system of equations using conventional methods (guass...) instead of LCP?
Thanks.

[Erin Catto]

Imagine you have a box sitting on a table. The table can exert force to hold the box up, but it cannot exert any force to hold the box down. That is the reason for the inequality constraints on the impulses.

[daniel_i_l]

Why do you need a force to hold the box down? Isn't that what gravity does?
Thanks.

[Eternl Knight]

What Erin is referring to is the fact that the table can only exert an upward/outward force on the box at the point of contact.

In a way this is kind of like the equation "box_bottom_coord >= table_top_coord". Notice the inequality in the equation.

An example of an equality constraint would be wanting the wheel to stay stuck to an axle, e.g. "wheel_center_coord = axle_end_coord".

Gravity is an additional "force" on the box, not a "constraint".

--EK

[Dirk Gregorius]

The force is there to hold the box up.

The gravity "pushes" the box in the ground. The contact force counter acts this (actio = reactio). If the box would have a velocity upwards there would be no force.