Celestial Mechanics

Using case 2, we calculated ratios of mass and velocity for each configuration. Using the following formula, we compared the ratio of mass and ratio of velocity. We compared the ratios to see if momentum was conserved by seeing if the ratios agree within three times the percent uncertainty in the velocities.

Next, theoretical velocity values were calculated, first by finding starting value, then by multiplying it by reference velocities according to equation (10) and Table1:

Connect D to EE and G to HH. By the rigidity of the rotation, ∆GHI=∆GG.HH.I. In particular GH=GG.HH.

where x, y are the coordinates of the robot (point o) in the inertial frame. If the linear speed and angular velocity of the robot are v and ω, respectively, assuming no-slip on the wheels, the velocity components can be written as

calculated using the following relation: u = m , v = m . This discussion

Contents Introduction 1 Vectors in two and three dimensions 2 Complex numbers 3 Coordinate geometry and sketch graphs 4 Circular functions 5 Antidifferentiation 6 Integration 7 Differential equations 8 Kinematics 9 Vector calculus 10 Dynamics iv 1 12 26 40 53 62 70 79 86 92

In the equation above, I_ring^this the theoretical moment of inertia of the Ring, Mr is the mass of the ring, R_1^2 is the inner radius of the ring, and R_2^2 is the outer radius of the ring.

The objective of the experiment is to understand the meaning of displacement, average velocity, instantaneous velocity, average acceleration and instantaneous in one-dimensional motion. The first experiment was to calculate the average and instantaneous velocity. We first

For an impulsive transfer case, there are several works, which focused on finding an ana-lytical solution to the primer vector equation. In 1669, Prussing published his work on the analytical solution of the out of plane component circular rendezvous problem [27]. In 1991, Carter published his studies of the xed time linearised impulsive rendezvous

Figure 8. CH1 receives the observation time of the object from CM1 and CM2, (b) CM1 and CM2 are synchronizing their clocks [12].

The missile acceleration should nullify the line-of-sight (LOS) rate between the target and interceptor that is basic philosophy behind PN. Originally, PNG law creates angular velocity or acceleration commands perpendicular to the LOS (line of sight). If two bodies are closing on each other eventually they will intercept when there is no rotation in the line of sight (LOS) between the two bodies relative to the inertial space.

±rue velocity by 2 per cent for 10 deg misalignment and 6 p e r cent for 20 deg misalignment.

case of simple geometry, in which A interacts with B: but in a more complex

Department of Mechanical Engineering MENG 263 TUTORIAL 1 Q1. The motion of a particle is defined by the relation x 2t3 6t2 10, where x is expressed in m and t in seconds. Determine the time, position, and acceleration when v 0. ( Ans. x 2m, a 12 m/s2 ) Q2. The motion of a particle is defined by the relation x 2t3 -15t2 24t 4, where x is expressed in meters and t in seconds. Determine (a) when the velocity is zero, (b) the position and the total distance traveled when the acceleration is zero. (Ans. (a) 1s ,4s (b) 1.5m,24.5m) Q3. A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns red. The traffic light is timed to stay red for 24 s. If the motorist wishes

(ii) 22 × 3 × 13 (v) 17 × 19 × 23 (ii) LCM = 23460; HCF = 2 (ii) LCM = 1139; HCF = 1 7. 36 minutes