Engr Help

Center of Curvature - (continued)

Strategy for locating the center of curvature, C, r_c :

1. First note that r_c = r + ρ e_n where r = x_p(t) i + y_p(t) j

where r locates the point on the path where the center of curvature is to be calculated

2. To find C one needs to calculate ρ and e_n .

3. First find e_n by examining the change of e_t over a short period of time, dt.

Summary: e_n = de_t/dt/ |de_t/dt | where e_t = dr/dt / | dr/dt|

4. Next find ρ using a_n = v² / ρ

a_p = d²r/dt² and v = | dr/dt |

Then a_n = a_p • e_n . So ρ = v² / a_n

The result is r_c = r + v² /a_n e_n which holds for space curves as well.