function dydt = car_model_w_parameters (time, y, differential_ratio)

%CAR_MODEL_W_PARAMETERS A simple dynamic model for the drive train of a car
%   DYDT = CAR_MODEL_W_PARAMETERS ( T, Y, DIFFERENTIAL_RATIO ) implements a
%   system of two first order differential equations that describe the
%   forward motion of a car.  The gear ratio of the differential can be
%   provided as an additional input.  The shift velocities are updated
%   based on the differential_ratio to make sure maximum engine power is
%   maintained at all times.
%
%   Inputs:
%      T:         A time value at which the derivatives are computed
%                 (not used, since the differential equation is
%                 time-independent)
%      Y:         The state vector at which the derivatives are computed.
%                 The state vector consists of two elements; Y(1) is the
%                 car velocity in [m/s] and Y(2) is the car position in [m]
%      DIFFERENTIAL_RATIO:  The gear ratio of the differential
%                 [dimensionless]
%
%   Outputs:
%      DYDT:      A column vector with the derivative of the state vector;
%                 DYDT(1) is the acceleration of the car in [m/s2] and
%                 DYDT(2) is the velocity of the car in [m/s]
%
%   Assumptions:   
%             - The transmission and differential are loss-free
%             - The load consists only of air and tire resistance
%             - The car is driven at full throttle
%             - A torque converter is included in the model
%             - the tires don't slip
%
%% ME 2016
%% Fall 2007
%%
%% AUTHOR:  Chris Paredis
%%

% keep track of the number of times this function is called -- to answer
% question 4 of the assignment
global num_model_evals;
num_model_evals = num_model_evals + 1;

% define all the parameters
mass = 1650;
wheel_radius = 0.332; % in [m]
gear_ratios = [2.77 1.54 1 0.69];
% differential_ratio = 4.266; -- now provided as input
slope = 0;

% IMPORTANT:  to make the car perform well for different differential
% ratios, the shift velocities need to be updated.  The optimal shift
% velocities change linearly with the differential ratio
nominal_differential_ratio = 4.266;
nominal_shift_velocity = [61.6459 109.5366 166.3211]/3.6; % in [m/s]
shift_velocity = nominal_shift_velocity * nominal_differential_ratio ...
                 /differential_ratio;


% the state y consists of position and velocity of the car
car_vel_ms = y(1);
car_position = y(2); % not used anywhere

% determine the total ratio (transmission + differential + wheel)
if car_vel_ms > shift_velocity(3)
    transmission_ratio = gear_ratios(4);
elseif car_vel_ms > shift_velocity(2)
    transmission_ratio = gear_ratios(3);
elseif car_vel_ms > shift_velocity(1)
    transmission_ratio = gear_ratios(2);
else
    transmission_ratio = gear_ratios(1);
end

total_ratio = transmission_ratio*differential_ratio/wheel_radius;

% convert velocity into engine speed, into engine torque and back to force
% on the car
omega_tc = car_vel_ms * total_ratio;
%torque_tc = engine_w_torque_converter( omega_tc);
torque_tc = interp_engine_w_torque_converter( omega_tc);
force_wheel = torque_tc * total_ratio;

% combine everything in the car's differential equation
resistance_force = resistance_force_CJP(car_vel_ms,slope);
dvdt = (force_wheel - resistance_force)/mass;
dydt = [dvdt; car_vel_ms];

% for debugging purposes, uncomment the next line
%fprintf('%12g %12g %12g %12g %12g\n',time,car_vel_ms*3.6,transmission_ratio,resistance_force,force_wheel);