Navigation

Future Navigation

Use WASD to rotate the ship and arrow keys to move it. Configure parameters and start simulation.

Configuration

x_{0}

(m)

y_{0}

(m)

z_{0}

(m)

\\varphi

(°)

v_{0}

(m/s)

\\theta

(°)

m

(kg)

g

(m/s²)

Current Information

t

Time:

0.00 s

Sphere Position:

X:0.0 Y:0.0 Z:0.0

Ship Position:

X:0.0 Y:0.0 Z:0.0

E_k

Kinetic Energy:

200.00 J

E_p

Potential Energy:

0.00 J

E_t

Total Energy:

200.00 J

Absolute Info

y_{max}

Max Height:

10.2m

Max Pos:

X:20.4 Z:0.0

t_{max}

Time Max H:

1.44s

Final Pos:

X:40.8 Z:0.0

t_{floor}

Time Final:

2.88s

E_{k0}

Init Kinetic:

200.0J

E_{p0}

Init Potential:

0.0J

Controles de Nave

Rotación

Movimiento

W/S: Inclinar

A/D: Balanceo

↑/↓: Adelante/Atrás

←/→: Girar

Time Calculator

Time

t

:0.00 s

s

0 s2.88 s

Values at time $t$ = 0.00 s

x

0.00 m

y

0.00 m

z

0.00 m

v_x

14.14 m/s

v_y

14.14 m/s

v_z

0.00 m/s

v

20.00 m/s

E_k

200.00 J

E_p

0.00 J

E_t

200.00 J

Physics Formulas

Basic Motion

Initial Velocity

v_{0x} = v_{0} \cdot \cos(\varphi) \cdot \cos(\theta)

v_{0y} = v_{0} \cdot \sin(\varphi)

v_{0z} = v_{0} \cdot \cos(\varphi) \cdot \sin(\theta)

Position

x(t) = x_0 + v_{0x} \cdot t

y(t) = y_0 + v_{0y} \cdot t - \frac{1}{2} g t^2

z(t) = z_0 + v_{0z} \cdot t

Velocity

v_{x}(t) = v_{0x}

v_{y}(t) = v_{0y} - g \cdot t

v_{z}(t) = v_{0z}

Maximum Height

Peak Values

y_{max} = y_0 + \frac{v_{0y}^2}{2g}

t_{max} = \frac{v_{0y}}{g}

x_{max} = x_0 + v_{0x} \cdot t_{max}

z_{max} = z_0 + v_{0z} \cdot t_{max}

Peak Velocities

v_{x}(t_{max}) = v_{0x}

v_{y}(t_{max}) = 0

v_{z}(t_{max}) = v_{0z}

v(t_{max}) = \sqrt{v_{0x}^2 + v_{0z}^2}

Energy & Impact

Energy

E_k = \frac{1}{2} m v^2

E_p = m g y

E_t = E_k + E_p

Final Position

t_{floor} = \frac{v_{0y} + \sqrt{v_{0y}^2 + 2gy_0}}{g}

x_{final} = x_0 + v_{0x} \cdot t_{floor}

z_{final} = z_0 + v_{0z} \cdot t_{floor}

y_{final} = 0

Final Velocities

v_{x}(t_{floor}) = v_{0x}

v_{y}(t_{floor}) = v_{0y} - g \cdot t_{floor}

v_{z}(t_{floor}) = v_{0z}

Variables Legend

v₀ - Initial velocity

φ, θ - Angles

g - Gravity

t - Time

Eₖ - Kinetic energy

Eₚ - Potential energy

Eₜ - Total energy

m - Mass