Basic Physics

This subtopic is created for the basis of recording what HoverEX’s physics engine involves. It is also written in the hope that someone else writing simmilar physics simulation based game will benifit from this.

They are mainly High School stuffs.

Vector

The fundamental of physics. It basically represents a Spatial coordinate of a object with magnitude and direction. In mathematic form, it can be described in two form.

Polar Form:

FIXME: insert image to explain


tabular{000}{0000}{
d = magnitude
theta = direction}

Coordinate Form (X/Y):

FIXME: insert image to explain

tabular{000}{0000}{
V_x = {vector cast on X axis}
V_y = {vector cast on Y axis}}

Switching in between Polar and Coord


tabular{000}{0000}{
V_x = {d * cos theta}
V_y = {d * sin theta}}

Resultant Vector

The most basic stuff is the Resultant Vector:

FIXME: insert image to explain

R = U + V + W

To split them up to a formular calculatable with the respect of X and Y axis:

FIXME: insert image to explain


tabular{000}{0000}{
R_x = {U_x + V_x + W_x}
R_y = {U_y + V_y + W_y}}

Very important in Velocity and Force calculation.


tabular{000}{0000}{
{dR} = {U(dt) + V(dt) + W(dt)}
{} = {dt(U + V + W)}}

Where

dt = number of time unit

Hence:


tabular{000}{0000}{
dR_x = {dt(U_x + V_x + W_x)}
dR_y = {dt(U_y + V_y + W_y)}}

Velocity

Velocity defines the Vector quantity of Speed.

V = d / dt

Hence with respect to X and Y axis:


tabular{000}{0000}{
V_x = {d_x / dt}
V_y = {d_y / dt}}

Acceleration

Acceleration defines the incremental changes of a velocity over time.

a = V / t

Fomular in respect to X and Y axis:

tabular{000}{0000}{
a_x = {V_x / t}
a_y = {V_y / t}}

Force

Force is a concept of work or energy described in Vector quantity.

F = m * a

Or in respect to X and Y axis:

tabular{000}{0000}{
F_x = {m * a_x}
F_y = {m * a_y}}

Thrust

Thrust is always opposite to the force exerted to a mass.

F = -m * a

Friction

Friction is the non-conservative resistive force that occurs when two surfaces travel along each other when forced together.

FIXME: insert image to explain

Let,

  • F_f = {Friction Force}
  • F_p = {Force Perpendicular to the contact surface (normal force)}
  • u  = {coefficient of friction}
    • (value between 0.0 and 1.0; Typical materials are between 0.3 and 0.6)

Hence,


F_f = F_p * u

Friction is a magnitude force. The direction depends on the Resultant Force exerted on it where it is opposite of the Resultant Force direction.

Momentum

Momentum is a physical quantity related to the velocity and mass of an object.

p = m * v

In respect to X and Y axis,


tabular{000}{0000}{
p_x = {m * v_x}
p_y = {m * v_y}}

Momentum is vital in computing collision reaction.

Impulse

The change in momentum is called Impulse.

I = F * dt

In respect to X and Y axis,

tabular{000}{0000}{
I_x = {F_x * d_t}
I_y = {F_y * d_t}}
 
dev/basic_physics.txt · Last modified: 2005/10/19 17:37 by exiang
 
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